# Category:Measure of Limit of Decreasing Sequence of Measurable Sets

Jump to navigation
Jump to search

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.