1、Let (X,B,μ) be a finite measure space, and let
f:X→R be a measurable function. If f^{n} is integrable
for each n, then show that ∫f^{n}dμ=c (a constant) holds
for all n=1,2,3,... iff f=χ_{A} for some measurable subset
A of X.
(<=) 這個方向是顯然的。
(=>) 想了很久完全沒頭緒，因此想請教該如何下手。
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