Mathematics - Measure and Integration (English)

   Monday, May 05, 2025   

Starting a new Lecture Notes Series on Mathematics - Measure and Integration

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Mathematics - Measure and Integration By Lecture Notes together!

Lecture 1: Mod-01 Lec-01 Introduction ,Extended Real numbers

Lecture 2: Mod-01 Lec-02 Algebra and Sigma Algebra of a subset of a set

Lecture 3: Mod-01 Lec-03 Sigma Algebra generated by a class

Lecture 4: Mod-01 Lec-04 Monotone Class

Lecture 5: Mod-02 Lec-05 Set function

Lecture 6: Mod-02 Lec-06 The Length function and its properties

Lecture 7: Mod-02 Lec-07 Countably additive set functions on intervals

Lecture 8: Mod-02 Lec-08 Uniqueness Problem for Measure

Lecture 9: Mod-03 Lec-09 Extension of measure

Lecture 10: Mod-03 Lec-10 Outer measure and its properties

Lecture 11: Mod-03 Lec-11 Measurable sets

Lecture 12: Mod-04 Lec-12 Lebesgue measure and its properties

Lecture 13: Mod-04 Lec-13 Characterization of Lebesque measurable sets

Lecture 14: Mod-05 Lec-14 Measurable functions

Lecture 15: Mod-05 Lec-15 Properties of measurable functions

Lecture 16: Mod-05 Lec-16 Measurable functions on measure spaces

Lecture 17: Mod-06 Lec-17 Integral of non negative simple measurable functions

Lecture 18: Mod-06 Lec-18 Properties of non negative simple measurable functions

Lecture 19: Mod-06 Lec-19 Monotone convergence theorem & Fatou's Lemma

Lecture 20: Mod-06 Lec-20 Properties of Integral functions & Dominated Convergence Theorem

Lecture 21: Mod-06 Lec-21 Dominated Convergence Theorem and applications

Lecture 22: Mod-06 Lec-22 Lebesgue Integral and its properties

Lecture 23: Mod-06 Lec-23 Denseness of continuous function

Lecture 24: Mod-07 Lec-24 Product measures, an Introduction

Lecture 25: Mod-07 Lec-25 Construction of Product Measure

Lecture 26: Mod-07 Lec-26 Computation of Product Measure-I

Lecture 27: Mod-07 Lec-27 Computation of Product Measure-II

Lecture 28: Mod-07 Lec-28 Integration on Product spaces

Lecture 29: Mod-07 Lec-29 Fubini's Theorems

Lecture 30: Mod-08 Lec-30 Lebesgue Measure and integral on R2

Lecture 31: Mod-08 Lec-31 Properties of Lebesgue Measure and integral on Rn

Lecture 32: Mod-08 Lec-32 Lebesgue integral on R2

Lecture 33: Mod-09 Lec-33 Integrating complex-valued functions

Lecture 34: Mod-09 Lec-34 Lp - spaces

Lecture 35: Mod-09 Lec-35 L2(X,S,mue)

Lecture 36: Mod-10 Lec-36 Fundamental Theorem of calculas for Lebesgue Integral-I

Lecture 37: Mod-10 Lec-37 Fundamental Theorem of calculus for Lebesgue Integral-II

Lecture 38: Mod-10 Lec-38 Absolutely continuous measures

Lecture 39: Mod-10 Lec-39 Modes of convergence

Lecture 40: Mod-10 Lec-40 Convergence in Measure