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A field of mathematics concerning measures, which are functions mapping sets to real numbers that generalize the idea of area and volume. Measure theory underlies modern treatments of probability. Questions about measure theory with a weak connection to probability or statistics may be more suitable for math.stackexchange.com than this site.
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Definition of sample space
The basic intuition is that:
$\Omega$ is the set of outcomes that can happen.
$\mathcal S$, a $\sigma$-field of subsets of $\Omega$, represents what information is available. It represents what outc …