Definition:Infinite Measure

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Definition

Let $\struct {X, \Sigma}$ be a measurable space.


Then the infinite measure is the measure defined by:

$\mu: \Sigma \to \overline \R, \ \map \mu E := \begin{cases} 0 & : \text{if } E = \O \\ +\infty & : \text{otherwise}\end{cases}$

where $\overline \R$ denotes the extended real numbers.


Also known as

The infinite measure is sometimes referred to as the trivial measure, but such can cause confusion with the null measure.


Also see


Sources