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MeasurableSpace
A measurable space is a foundational concept in measure theory. It provides the structure needed to define and work with measures, which are generalizations of intuitive notions such as length, area, and volume.
A measurable space is an ordered pair
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$X$ is a set. -
$\mathcal{F}$ is a σ-algebra on$X$ .
The set
A collection
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$X$ itself is in$\mathcal{F}$ (i.e., the entire space is measurable). - If
$A$ is in$\mathcal{F}$ , then its complement$A^c$ is also in$\mathcal{F}$ . - If
$A_1, A_2, ... \in \mathcal{F}$ , then the countable union$\cup_{i=1}^{\infty}A_i$ is also in$\mathcal{F}$ .
The idea of a σ-algebra is to delineate which subsets of
Once you have a measurable space