Thursday, 12 April 2018

lebesgue integral - Condition for integrability on finite measure space

Let (X,F,μ) be a finite measure space. If f:XR is a measurable real function, show that, fL1(μ) iff n=0μ({fn})<. Am a bit stuck on the () direction so any help is appreciated, thanks.

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real analysis - How to find limhrightarrow0fracsin(ha)h

How to find limh0sin(ha)h without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...