![]() In general, if one wants to associate a consistent size to each subset of a given set while satisfying the other axioms of a measure, one only finds trivial examples like the counting measure. ![]() It must further be countably additive: the measure of a 'large' subset that can be decomposed into a finite (or countably infinite) number of 'smaller' disjoint subsets is equal to the sum of the measures of the 'smaller' subsets. Technically, a measure is a function that assigns a non-negative real number or +∞ to (certain) subsets of a set X ( seeDefinition below).
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