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
- 2005: René L. Schilling: Measures, Integrals and Martingales ... (previous) ... (next): $4.7 \ \text{(v)}$