Category:Measure of Limit of Decreasing Sequence of Measurable Sets
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This category contains pages concerning Measure of Limit of Decreasing Sequence of Measurable Sets:
Let $\struct {X, \Sigma, \mu}$ be a measure space.
Let $E \in \Sigma$.
Let $\sequence {E_n}_{n \mathop \in \N}$ be an decreasing sequence of $\Sigma$-measurable sets such that:
- $E_n \downarrow E$
where $E_n \downarrow E$ denotes the limit of decreasing sequence of sets.
Suppose also that $\map \mu {E_1} < \infty$.
Then:
- $\ds \map \mu E = \lim_{n \mathop \to \infty} \map \mu {E_n}$
Pages in category "Measure of Limit of Decreasing Sequence of Measurable Sets"
The following 2 pages are in this category, out of 2 total.