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
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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
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
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
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])<ε,下面仅对A交[a,b]讨论即可.取一个k,满足(b-a)/k<ε的k(固定下来).再[a,b]中加入k个等分点,分成的小区间记成[a_i,b_i],记A_i=A交[a_i,b_i],那么A=A_i的并再并（A-[a,b]）,每个测度不超过ε,且为有限个,K+1个.至于不相交
的问题,主要在[a_i,b_i]的端点,这个处理一下即可,需要的话改成半开半闭的.
你上个题还有分,这个没了