Measure Theory 7: Lebesgue Measurable Sets -1

We start with a less stringent definition of Lebesgue measurable sets. We prove that any interval is measurable and any set of outer measure zero is measurable. Then we establish the equivalence of our definition with a more stringent definition due to Caratheodary.
Timestamp by Kogularaj K.
02:06 - Recall
03:37 - Motivation for the definition of measurable sets
04:25 - Definition of measurable sets
09:14 - Measurability of sets with zero outer measure
12:40 - Notation for class of measurable subsets
12:55 - Uncountability of the class
14:30 - Definition of Lebesgue measure
16:07 - Measurability of complement of measurable sets
20:17 - Measurability of intervals in R
34:23 - Caratheodary’s Definition of measurable sets
37:44 - Equivalence of the two definitions
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[@kumarhcu]

Please send me a Timestamp. Thanks.

[@KogularajK.]

02:06 - Recall
03:37 - Motivation for the definition of measurable sets
04:25 - Definition of measurable sets
09:14 - Measurability of sets with zero outer measure
12:40 - Notation for class of measurable subsets
12:55 - Uncountability of the class
14:30 - Definition of Lebesgue measure
16:07 - Measurability of complement of measurable sets
20:17 - Measurability of intervals in R
34:23 - Caratheodary’s Definition of measurable sets
37:44 - Equivalence of the two definitions

[@kumarhcu]

@@KogularajK. Thanks.

[@KogularajK.]

@@kumarhcu You are most welcome, sir. 😊

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Thank you for everything.

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[@thakursharwan8888]

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Pranamam Acharya

[@abdurrahmanlabib916]

Sir when will Measure Theory, Analysis on R^n book be published?

[@souravsadhukhan3077]

Sir,are you following approach of Royden?

[@shashidhar531]

Thank you sir