Answer to Question #310729 in Real Analysis for ABC2468

Question #310729

Show that the union of two sets, each of measure zero, has measure zero

Expert's answer

By monotonicity and non-negativity of the measure: Let "\\mu A=0,\\ \\mu B=0":

"0\\leq\\mu(A\\cup B)\\leq\\mu A+\\mu B=0\\Rightarrow\\mu(A\\cup B)=0"

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