Category:Outer Measure of Limit of Increasing Sequence of Sets

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This category contains pages concerning Outer Measure of Limit of Increasing Sequence of Sets:


Let $\mu^*$ be an outer measure on a set $X$.

Let $\sequence {S_n}$ be an increasing sequence of $\mu^*$-measurable sets, and let $S_n \uparrow S$ (as $n \to \infty$).


Then for any subset $A \subseteq X$:

$\ds \map {\mu^*} {A \cap S} = \lim_{n \mathop \to \infty} \map {\mu^*} {A \cap S_n}$

Pages in category "Outer Measure of Limit of Increasing Sequence of Sets"

The following 2 pages are in this category, out of 2 total.