Probability Space

A probability space (or probability tiple) is the structure $(S,\mathcal{F},P)$ used to model random experiments.

• $S$: the Sample Space, the set of all possible outcomes.
• $\mathcal{F}$: a [[10 Zettels/20251114-092453|$\sigma$-algebra]] of subsets of $S$, representing the events we can assign probabilities to.
• $P$: a probability measure, a function that assigns a probability to each event in $\mathcal{F}$, satisfying the axioms of probability.

note: sometimes $S$ is also denoted $\Omega$