实变函数证明题求助!Show that if A has finite measure and ε>0,then A i

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实变函数证明题求助!
Show that if A has finite measure and ε>0,then A is the disjoint union of a finite number of measurable sets,each of which has measure at nost ε.
翻译:证明:如果A有有限测度,ε>0,那么A是有有限个不相交的可测集的并,每一个可测集有最大测度ε

我不知道你用的那个版本,测度背景等我不清楚,我以一维勒贝格测度为例证明：
因为A有有限测度,由测度定义知道,对任意ε>0,存在a,b,满足m(A-[a,b])

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