Category:Outer Measure of Limit of Increasing Sequence of Sets
Jump to navigation
Jump to search
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.