Definition (probability space):

A probability space is a measure space ${\displaystyle (\Omega ,{\mathcal {F}},\mathbb {P} )}$, ${\displaystyle \Omega }$ being the set, ${\displaystyle {\mathcal {F}}}$ the ${\displaystyle \sigma }$-algebra and ${\displaystyle \mathbb {P} }$ the measure, such that the mass of ${\displaystyle \mathbb {P} }$ equals ${\displaystyle 1}$.

Definition (probability measure):

The measure of a probability space is called probability measure.

Definition (event):

An element of the ${\displaystyle \sigma }$-algebra of a probability space is called an event.