Probabilistic space

It is a measure space with a selected probability measure. That is, $(\mathrm{\Omega },\mathcal{F},\mathbb{P})$, where:

• $\mathrm{\Omega }$ is the sample space (set of all possible outcomes),
• $\mathcal{F}$ is a $\sigma$-algebra (set of possible events),
• $\mathbb{P}$ is a probability measure,
• $T$ is an index set (often representing time, e.g., $T=\mathbb{N}$ or $T=[0,\mathrm{\infty })$).