# counting measure

Let $(X,\mathfrak{B})$ be a measurable space. The measure $\mu$ on $X$ defined by

 $\mu(A)=\left\{\begin{array}[]{ll}n&\text{if}\,A\,\text{ has exactly }\,n\,% \text{ elements}\\ \infty&\text{otherwise.}\end{array}\right.$

for all $A\in\mathfrak{B}$ is called the counting measure on $X$. Usually this is applied when $X$ is countable, e.g. $\mathbb{N}$ or $\mathbb{Z}$.

Title counting measure CountingMeasure 2013-03-22 12:21:52 2013-03-22 12:21:52 mathwizard (128) mathwizard (128) 7 mathwizard (128) Definition msc 28A12 Measure