Lecture 8: Lebesgue Measurable Subsets and Measure

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MIT 18.102 Introduction to Functional Analysis, Spring 2021
Instructor: Dr. Casey Rodriguez
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We continue our discussion of sigma-algebras and measure, including fundamental examples of measurable sets that which will allow us to define the Lebesgue measure. We then turn to proving properties of Lebesgue measure.
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Опубликовано:

21 окт 2024

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Комментарии : 10

@sunritroykarmakar4406 4 месяца назад

Amazing lecture . Really solid

@thiennhatvuong4055 Год назад

@MITOCW can you up the course Real Analysis 18.100B?

@KrazyKittyTailz Месяц назад

What exactly is the difference between 18.100A (which I've taken) and 18.100B? Seems that MIT subsections quite a lot of its math courses!

@hausdorffm Год назад

I really like this lecture! I went over what I learnt in lectures long ago. 43:45 It is boring thing, but the third equality in the estimate of m(A_1) + m(A_2) at 43:45 is not correct or not necessary. Since length(I_n) = length(J_n) + length(K_n) and the definition of I_n, we should omit the third equality from the estimation of m(A_1) + m(A_2).

@carl3260 6 месяцев назад

Not sure this is right, the chain seems correct: measure of A_1,A_2 ---> measure of J,K ---> length of J,K ---> length of Is ---> measure of A (but, the epsilon at 44:06 shouldn't be there and Is should be defined at the start such that their union contains A)