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Consider a sample space \(\; \Omega = \left\{ \omega \right\} \;\) and an associated sigma algebra \(\; \mathcal{F} \;\). A measurable space is simply the tuple
\[
\left( \Omega, \mathcal{F} \right).
\]
NOTE In spite of the name, the measurable space does not include a measure \(\; P \;\). If we included the measure, then we would get a probability space.
1 https://en.wikipedia.org/wiki/Measurable_space