Modules / Lectures

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noc20_ma44_assignment_Week_0 | noc20_ma44_assignment_Week_0 |

noc20_ma44_assignment_Week_1 | noc20_ma44_assignment_Week_1 |

noc20_ma44_assignment_Week_10 | noc20_ma44_assignment_Week_10 |

noc20_ma44_assignment_Week_11 | noc20_ma44_assignment_Week_11 |

noc20_ma44_assignment_Week_12 | noc20_ma44_assignment_Week_12 |

noc20_ma44_assignment_Week_2 | noc20_ma44_assignment_Week_2 |

noc20_ma44_assignment_Week_3 | noc20_ma44_assignment_Week_3 |

noc20_ma44_assignment_Week_4 | noc20_ma44_assignment_Week_4 |

noc20_ma44_assignment_Week_5 | noc20_ma44_assignment_Week_5 |

noc20_ma44_assignment_Week_6 | noc20_ma44_assignment_Week_6 |

noc20_ma44_assignment_Week_7 | noc20_ma44_assignment_Week_7 |

noc20_ma44_assignment_Week_8 | noc20_ma44_assignment_Week_8 |

noc20_ma44_assignment_Week_9 | noc20_ma44_assignment_Week_9 |

Sl.No | Chapter Name | MP4 Download |
---|---|---|

1 | Finite Sets and Cardinality | Download |

2 | Infinite Sets and the Banach-Tarski Paradox - Part 1 | Download |

3 | Infinite Sets and the Banach-Tarski Paradox - Part 2 | Download |

4 | Elementary Sets and Elementary measure - Part 1 | Download |

5 | Elementary Sets and Elementary measure - Part 2 | Download |

6 | Properties of elementary measure - Part 1 | Download |

7 | Properties of elementary measure - Part 2 | Download |

8 | Uniqueness of elementary measure and Jordan measurability - Part 1 | Download |

9 | Uniqueness of elementary measure and Jordan measurability - Part 2 | Download |

10 | Characterization of Jordan measurable sets and basic properties of Jordan measure - Part 1 | Download |

11 | Characterization of Jordan measurable sets and basic properties of Jordan measure - Part 2 | Download |

12 | Examples of Jordan measurable sets- I | Download |

13 | Examples of Jordan measurable sets- II - Part 1 | Download |

14 | Examples of Jordan measurable sets- II - Part 2 | Download |

15 | Jordan measure under Linear transformations - Part 1 | Download |

16 | Jordan measure under Linear transformations - Part 2 | Download |

17 | Connecting the Jordan measure with the Riemann integral - Part 1 | Download |

18 | Connecting the Jordan measure with the Riemann integral - Part 2 | Download |

19 | Outer measure - Motivation and Axioms of outer measure | Download |

20 | Comparing Inner Jordan measure, Lebesgue outer measure and Jordan Outer measure | Download |

21 | Finite additivity of outer measure on Separated sets, Outer regularity - Part 1 | Download |

22 | Finite additivity of outer measure on Separated sets, Outer regularity - Part 2 | Download |

23 | Lebesgue measurable class of sets and their Properties - Part 1 | Download |

24 | Lebesgue measurable class of sets and their Properties - Part 2 | Download |

25 | Equivalent criteria for lebesgue measurability of a subset - Part 1 | Download |

26 | Equivalent criteria for lebesgue measurability of a subset - Part 2 | Download |

27 | The measure axioms and the Borel-Cantelli Lemma | Download |

28 | Properties of the Lebesgue measure: Inner regularity,Upward and Downwar Monotone convergence theorem, and Dominated convergence theorem for sets - Part 1 | Download |

29 | Properties of the Lebesgue measure: Inner regularity,Upward and Downwar Monotone convergence theorem, and Dominated convergence theorem for sets - Part 2 | Download |

30 | Lebesgue measurability under Linear transformation, Construction of Vitali Set -Part 1 | Download |

31 | Lebesgue measurability under Linear transformation, Construction of Vitali Set - Part 2 | Download |

32 | Abstract measure spaces: Boolean and Sigma-algebras | Download |

33 | Abstract measure and Caratheodory Measurability - Part 1 | Download |

34 | Abstract measure and Caratheodory Measurability - Part 2 | Download |

35 | Abstrsct measure and Hahn-Kolmogorov Extension | Download |

36 | Lebesgue measurable class vs Caratheodory extension of usual outer measure on R^d | Download |

37 | Examples of Measures defined on R^d via Hahn Kolmogorov extension - Part 1 | Download |

38 | Examples of Measures defined on R^d via Hahn Kolmogorov extension - Part 2 | Download |

39 | Measurable functions: definition and basic properties - Part 1 | Download |

40 | Measurable functions: definition and basic properties - Part 2 | Download |

41 | Egorov's theorem: abstract version | Download |

42 | Lebesgue integral of unsigned simple measurable functions: definition and properties | Download |

43 | Lebesgue integral of unsigned measurable functions: motivation, definition and basic properties | Download |

44 | Fundamental convergence theorems in Lebesgue integration: Monotone convergence theorem, Tonelli's theorem and Fatou's lemma | Download |

45 | Lebesgue integral for complex and real measurable functions: the space of L^1 functions | Download |

46 | Basic properties of L^1-functions and Lebesgue's Dominated convergence theorem | Download |

47 | L^1 functions on R^d: Egorov's theorem revisited (Littlewood's third principle) | Download |

48 | L^1 functions on R^d: Statement of Lusin's theorem (Littlewood's second principle), Density of simple functions, step functions, and continuous compactly supported functions in L^1 | Download |

49 | L^1 functions on R^d: Proof of Lusin's theorem, space of L^1 functions as a metric space | Download |

50 | L^1 functions on R^d: the Riesz-Fischer theorem | Download |

51 | Various modes of convergence of measurable functions | Download |

52 | Easy implications from one mode of convergence to another | Download |

53 | Implication map for modes of convergence with various examples | Download |

54 | Uniqueness of limits across various modes of convergence | Download |

55 | Some criteria for reverse implications for modes of convergence | Download |

56 | Riesz Representation theorem- Motivation | Download |

57 | Basics on Locally compact Hausdorff spaces | Download |

58 | Borel and Radon measures on LCH spaces | Download |

59 | Properties of Radon measures and Lusin's theorem on LCH spaces | Download |

60 | Riesz Representation theorem - Complete statement and proof - Part 1 | Download |

61 | Riesz Representation theorem - Complete statement and proof - Part 2 | Download |

62 | Examples of measures constructed using RRT | Download |

63 | Theorems of Tonelli and Fubini- interchanging the order of integration for repeated integrals: motivation and discussion of product measure spaces | Download |

64 | Product measures | Download |

65 | Tonelli's theorem for sets - Part 1 | Download |

66 | Tonelli's theorem for sets - Part 2 | Download |

67 | Fubini-Tonelli theorem: interchanging order of integration for measurable and L^1 functions on sigma-finite measure spaces | Download |

68 | Lebesgue's differentiation theorem: introduction and motivation | Download |

69 | Lebesgue's differentiation theorem: statement and proof - Part 1 | Download |

70 | Lebesgue's differentiation theorem: statement and proof - Part 2 | Download |

71 | DIfferentiation theorems: Almost everywhere differentiability for Monotone and Bounded Variation functions - Part 1 | Download |

72 | DIfferentiation theorems: Almost everywhere differentiability for Monotone and Bounded Variation functions - Part 2 | Download |

73 | Riesz's Rising Sun Lemma | Download |

74 | Differentiation theorem for monone continuous functions | Download |

75 | Differentation theorem for general monotone functions and Second fundamental theorem of calculus for absolutely continuous functions | Download |

Sl.No | Chapter Name | English |
---|---|---|

1 | Finite Sets and Cardinality | Download Verified |

2 | Infinite Sets and the Banach-Tarski Paradox - Part 1 | Download Verified |

3 | Infinite Sets and the Banach-Tarski Paradox - Part 2 | Download Verified |

4 | Elementary Sets and Elementary measure - Part 1 | Download Verified |

5 | Elementary Sets and Elementary measure - Part 2 | Download Verified |

6 | Properties of elementary measure - Part 1 | Download Verified |

7 | Properties of elementary measure - Part 2 | Download Verified |

8 | Uniqueness of elementary measure and Jordan measurability - Part 1 | PDF unavailable |

9 | Uniqueness of elementary measure and Jordan measurability - Part 2 | PDF unavailable |

10 | Characterization of Jordan measurable sets and basic properties of Jordan measure - Part 1 | PDF unavailable |

11 | Characterization of Jordan measurable sets and basic properties of Jordan measure - Part 2 | PDF unavailable |

12 | Examples of Jordan measurable sets- I | PDF unavailable |

13 | Examples of Jordan measurable sets- II - Part 1 | PDF unavailable |

14 | Examples of Jordan measurable sets- II - Part 2 | PDF unavailable |

15 | Jordan measure under Linear transformations - Part 1 | PDF unavailable |

16 | Jordan measure under Linear transformations - Part 2 | PDF unavailable |

17 | Connecting the Jordan measure with the Riemann integral - Part 1 | PDF unavailable |

18 | Connecting the Jordan measure with the Riemann integral - Part 2 | PDF unavailable |

19 | Outer measure - Motivation and Axioms of outer measure | PDF unavailable |

20 | Comparing Inner Jordan measure, Lebesgue outer measure and Jordan Outer measure | PDF unavailable |

21 | Finite additivity of outer measure on Separated sets, Outer regularity - Part 1 | PDF unavailable |

22 | Finite additivity of outer measure on Separated sets, Outer regularity - Part 2 | PDF unavailable |

23 | Lebesgue measurable class of sets and their Properties - Part 1 | PDF unavailable |

24 | Lebesgue measurable class of sets and their Properties - Part 2 | PDF unavailable |

25 | Equivalent criteria for lebesgue measurability of a subset - Part 1 | PDF unavailable |

26 | Equivalent criteria for lebesgue measurability of a subset - Part 2 | PDF unavailable |

27 | The measure axioms and the Borel-Cantelli Lemma | PDF unavailable |

28 | Properties of the Lebesgue measure: Inner regularity,Upward and Downwar Monotone convergence theorem, and Dominated convergence theorem for sets - Part 1 | PDF unavailable |

29 | Properties of the Lebesgue measure: Inner regularity,Upward and Downwar Monotone convergence theorem, and Dominated convergence theorem for sets - Part 2 | PDF unavailable |

30 | Lebesgue measurability under Linear transformation, Construction of Vitali Set -Part 1 | PDF unavailable |

31 | Lebesgue measurability under Linear transformation, Construction of Vitali Set - Part 2 | PDF unavailable |

32 | Abstract measure spaces: Boolean and Sigma-algebras | PDF unavailable |

33 | Abstract measure and Caratheodory Measurability - Part 1 | PDF unavailable |

34 | Abstract measure and Caratheodory Measurability - Part 2 | PDF unavailable |

35 | Abstrsct measure and Hahn-Kolmogorov Extension | PDF unavailable |

36 | Lebesgue measurable class vs Caratheodory extension of usual outer measure on R^d | PDF unavailable |

37 | Examples of Measures defined on R^d via Hahn Kolmogorov extension - Part 1 | PDF unavailable |

38 | Examples of Measures defined on R^d via Hahn Kolmogorov extension - Part 2 | PDF unavailable |

39 | Measurable functions: definition and basic properties - Part 1 | PDF unavailable |

40 | Measurable functions: definition and basic properties - Part 2 | PDF unavailable |

41 | Egorov's theorem: abstract version | PDF unavailable |

42 | Lebesgue integral of unsigned simple measurable functions: definition and properties | PDF unavailable |

43 | Lebesgue integral of unsigned measurable functions: motivation, definition and basic properties | PDF unavailable |

44 | Fundamental convergence theorems in Lebesgue integration: Monotone convergence theorem, Tonelli's theorem and Fatou's lemma | PDF unavailable |

45 | Lebesgue integral for complex and real measurable functions: the space of L^1 functions | PDF unavailable |

46 | Basic properties of L^1-functions and Lebesgue's Dominated convergence theorem | PDF unavailable |

47 | L^1 functions on R^d: Egorov's theorem revisited (Littlewood's third principle) | PDF unavailable |

48 | L^1 functions on R^d: Statement of Lusin's theorem (Littlewood's second principle), Density of simple functions, step functions, and continuous compactly supported functions in L^1 | PDF unavailable |

49 | L^1 functions on R^d: Proof of Lusin's theorem, space of L^1 functions as a metric space | PDF unavailable |

50 | L^1 functions on R^d: the Riesz-Fischer theorem | PDF unavailable |

51 | Various modes of convergence of measurable functions | PDF unavailable |

52 | Easy implications from one mode of convergence to another | PDF unavailable |

53 | Implication map for modes of convergence with various examples | PDF unavailable |

54 | Uniqueness of limits across various modes of convergence | PDF unavailable |

55 | Some criteria for reverse implications for modes of convergence | PDF unavailable |

56 | Riesz Representation theorem- Motivation | PDF unavailable |

57 | Basics on Locally compact Hausdorff spaces | PDF unavailable |

58 | Borel and Radon measures on LCH spaces | PDF unavailable |

59 | Properties of Radon measures and Lusin's theorem on LCH spaces | PDF unavailable |

60 | Riesz Representation theorem - Complete statement and proof - Part 1 | PDF unavailable |

61 | Riesz Representation theorem - Complete statement and proof - Part 2 | PDF unavailable |

62 | Examples of measures constructed using RRT | PDF unavailable |

63 | Theorems of Tonelli and Fubini- interchanging the order of integration for repeated integrals: motivation and discussion of product measure spaces | PDF unavailable |

64 | Product measures | PDF unavailable |

65 | Tonelli's theorem for sets - Part 1 | PDF unavailable |

66 | Tonelli's theorem for sets - Part 2 | PDF unavailable |

67 | Fubini-Tonelli theorem: interchanging order of integration for measurable and L^1 functions on sigma-finite measure spaces | PDF unavailable |

68 | Lebesgue's differentiation theorem: introduction and motivation | PDF unavailable |

69 | Lebesgue's differentiation theorem: statement and proof - Part 1 | PDF unavailable |

70 | Lebesgue's differentiation theorem: statement and proof - Part 2 | PDF unavailable |

71 | DIfferentiation theorems: Almost everywhere differentiability for Monotone and Bounded Variation functions - Part 1 | PDF unavailable |

72 | DIfferentiation theorems: Almost everywhere differentiability for Monotone and Bounded Variation functions - Part 2 | PDF unavailable |

73 | Riesz's Rising Sun Lemma | PDF unavailable |

74 | Differentiation theorem for monone continuous functions | PDF unavailable |

75 | Differentation theorem for general monotone functions and Second fundamental theorem of calculus for absolutely continuous functions | PDF unavailable |

Sl.No | Language | Book link |
---|---|---|

1 | English | Not Available |

2 | Bengali | Not Available |

3 | Gujarati | Not Available |

4 | Hindi | Not Available |

5 | Kannada | Not Available |

6 | Malayalam | Not Available |

7 | Marathi | Not Available |

8 | Tamil | Not Available |

9 | Telugu | Not Available |