Lecture Notes

Study Material

Dear Students,

All of you are requested to kindly go through the books as given in your course syllabus. These notes has been prepared from the same books (taking in to account the syllabus of the course) but there may be some useful information (available in those book) that may be missing in these lecture notes. In any case if you are reading these notes then for any comments, suggestions or error you can contact me at email id: jkaur@thapar.edu

Videos

Lecture Notes

Unit-I (outer measure)

• First lecture(outer measure)

• 2nd lecture(outer measure)

• 3rd Lecture (Lebesgue Measurable sets)

• 4th Lecture (m'ble sets)

• 5th Lecture (m'ble sets)

• 6th Lecture(borel sets)

• 7th Lecture(monotone sequence)

• 8th Lecture( characterization of m'ble sets)

• 9th Lecture(Non-measurable sets)

Unit-II( Measurable functions)

• notes on Measurable functions, step function, properties

• notes on Convergence in measure and related theorems

Unit-III (Lebesgue Integral)

• notes on Lebesgue integral (definition )

• notes on Lebesgue integral

• Notes on Bounded convergence Theorem

• Notes on Lebesgue integral of Non-negative functions

• Notes on Fatou's lemma and related theorems

• Notes on Monotone convergence theorem and related results

• Notes on General Lebesgue Integral

• Properties of General Lebesgue integral

• Lebesgue dominated convergence theorem

Unit -IV (Differentiation and Integration)

• Dini derivatives

• Bounded Variation and their related theorems

• Jordan Decomposition Theorem and related results

• Indefinite Integral and related Theorems

• Absolutely continuity with theorems