probability space

Definition

The probability space $(S,\mathcal{F},P)$ is defined over universal set $S$ (the sample space in probability theory serves as the universal set from set theory in this context), Borel field of events $\mathcal{F}$ (the event space), and probabilities of these events $P$ (probability measure, which is a measure space).

Condensed definition: a probability space is a measure space where measure of the whole space is equal to one

References

1. https://en.wikipedia.org/wiki/Probability_space
2. https://mathoverflow.net/questions/31603/why-do-probabilists-take-random-variables-to-be-borel-and-not-lebesgue-measura/31724#31724
3. https://en.wikipedia.org/wiki/Probability_measure