Lebesgue Measurable function

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0:00 : lesbugue measurable function
2:32 : equivalent conditions for measurable functions.
12:05 : An important Remark regarding a necessary condition for measurable function .

Thanks for the beautiful lecture.

dipsacedemy
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Sir if the elements of set E that satisfy the given condition beleongs to set A the how that elements are measurabla?A is sigma algebra and the elements which belongs to sigma algebra are measurable? kindly explain my point

aminasheikh