# Measure space

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In mathematics, a measure space is a triple ${\displaystyle \scriptstyle (\Omega ,{\mathcal {F}},\mu )}$ where ${\displaystyle \scriptstyle \Omega }$ is a set, ${\displaystyle \scriptstyle {\mathcal {F}}}$ is a sigma algebra of subsets of ${\displaystyle \scriptstyle \Omega }$ and ${\displaystyle \mu }$ is a measure on ${\displaystyle \scriptstyle {\mathcal {F}}}$. If ${\displaystyle \mu }$ satisfies ${\displaystyle \scriptstyle \mu (\Omega )=1}$ then the measure space is called a probability space.