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Lec-3 application of Shapiro's tauberian theorem

Lec-2 Euler's summation formula

Lec-18 (part-1) Reisz fisher's theorem

Lec-17 part-2

Lec-16 ( part-1) definition of summable and absolutely summable and based on theorem

Lec-15 minkowski's inequality

Part-2 of holders inequality

Holders inequality part-1(lec-14)

Lec-13 Case -2 of norm on L^p spaces

Lec-12 Theorem based on norm on L^p space

Lec-11 Definitions of L^p space, essentially bounded and essential supremum

Lec-10 Part-2 of theorem 3

Lec-8 if f is absolutely continuous functn then f is function of bounded variation

Lec-9,f indfnte intgrll of lebesgue integrable function whenever f is a absolutely continuous funct

Lec-7 Definition of absolute continuity and based on theorem

Lec-6 Part-2

Lec-5 Theorem based on indefinite integral part -1

Lec-4 Part-2

Lec-3 f is function of bounded variation then F is differentiable and F`=f almost everywhere part -1

Lec-2 if f is lebesgue Integrable then f =0 almost everywhere

Unit-4 lec-1 Definition of indefinite integral And based on theorem

Dini derivatives

If f is function of bounded variation then f is differential almost everywhere

Jordan decomposition theorem part -2

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