Measure and Integration 10 - Littlewood Three Principle

In this lecture, we discuss some properties of measurable functions and Littlewood Three Principles related to measurable sets and measurable functions.
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[@sanjaykumar-mg2iv]

have you discussed lusin"s theorem

[@prafullgupta7924]

Sir at 31.09 , how can you write that , If x does not belongs to UGk , k≥N , then x does not belong to Gk for some k≥N ?
If it's not in union , then it will not be in any set for k≥N

[@BSReddy.Tech4Trends]

Yes, x is not in every set of the union. Then no need to use the monotonicity of E_n. Thanks for the correction.

[@siyasingh9530]

Thank you sir for best explanation

[@BSReddy.Tech4Trends]

Please share my channel with your contacts.

[@mathematicalminds8446]

sir what is meant the " nearly" in littlewood principle

[@BSReddy.Tech4Trends]

Nearly means measure of their difference is less than epsilon.
For example , measurable function f is nearly a continuous function g means m*(f-g)

[@BSReddy.Tech4Trends]

Vitali covering lemma is the precise statement of measurable set is nearly finite union of disjoint intervals.