MATH: P-3 Real Analysis and Measure Theory (e-PGP) (English)

   Wednesday, December 21, 2022   

Starting a new Lecture Notes Series on MATH: P-3 Real Analysis and Measure Theory (e-PGP)

Youtube Lecture Playlist Credits 

Channel Name: Vidya-mitra

So Let Us Start to This Journey of Learning
MATH: P-3 Real Analysis and Measure Theory (e-PGP)
By Lecture Notes together!

Lecture Description of this above Topic:

Lecture 1: Lebesgue measurable sets and their properties (MAT)

Lecture 2: Notion of lebesgue measure and its basic properties (MAT)

Lecture 3: Lebesgue measurable functions and basic properties (MAT)

Lecture 4: Lebesgue measurable functions: almost everywhere concept and its implications (MAT)

Lecture 5: Simple functions as building blocks of lebesgue measurable functions (MAT)

Lecture 6: Relation between almost everywhere convergence and convergence in measure

Lecture 7: Lebesgue integration of bounded measurable functions: Riemann integration and lebesgue integration

Lecture 8: Convergence of sequences of measurable functions

Lecture 9: Lebesgue integral of non-negative functions and Monotone Convergence Theorem (MAT)

Lecture 10: Most general notion of Lebesgue integrability and ominated convergence theorem (MAT)

Lecture 11: Fatou's Lemma and notion of Lebesgue integrable functions

Lecture 12: Functions of bounded variations (MAT)

Lecture 13: Functions of bounded variations and associated concepts: Vitali Covering Theorem (MAT)

Lecture 14: Functions of bounded variations and associated concepts: absolutely continuous functions (MAT)

Lecture 15: Functions of bounded variations and associated concepts: differentiability (MAT)

Lecture 16: Some useful results of Lebesgue integration (MAT)

Lecture 17: Fundamental Theorem of Integral Calculus for lebesgue integration (MAT)

Lecture 18: Abstract measure and abstract outer measure (MAT)

Lecture 19: Abstract measure theory: extension of measure and the notion measurable covers (MAT)

Lecture 20: Abstract measure theory: complete measure and the notion of completion (MAT)

Lecture 21: Riemann-Stieltjes integral and its basic properties (MAT)

Lecture 22: Notion of Darbaux Stieltjes integral and its implications (MAT)

Lecture 23: Motivation and introduction of the notion of Lebesgue integration of bounded functions (MAT)

Lecture 24: Examples and some further observations on measurable sets (MAT)

Lecture 25: Fundamental Theorem of Integral Calculus for Riemann integration and it's deficiency (MAT)

Lecture 26: Lebesgue measure: existence of a non-measurable set (MAT)

Lecture 27: Lebesgue measure: characterization of measurable sets and further observations (MAT)

Lecture 28: Lebesgue measure: notion of inner measure (MAT)

Lecture 29: Lebesgue outer measure: definition and properties (MAT)

Lecture 30: Abstract measure theory: rings and σ-rings (MAT)

Lecture 31: Lebesgue integration of bounded measurable functions: equivalence (MAT)

Lecture 32: Convergence of sequences of measurable functions: almost uniform convergence (MAT)

Lecture 33: Abstract measure theory: monotone classes (MAT)

Lecture 34: Further results on absolutely continuous functions and Dini's Derivates (MAT)