Space probabilisable

A space probabilisable is a couple $\backslash \; left\; (\backslash \; Omega,\; \backslash \; mathcal\; B\; \backslash \; right)$ made of a Ensemble Ω , of a tribe or σ-algebra $\backslash \; mathcal\; B$ on Ω .

The unit Ω is called the universe and the elements of $\backslash \; mathcal\; B$ are called the events.

Exemples :

• Is Ω an unspecified universe; $\backslash \; left\; (\backslash \; Omega,\; \backslash \; mathcal\; P\; (\backslash \; Omega)\; \backslash \; right)$ is a space probabilisable. This example is important since if Ω is countable then all generated Tribu by the elementary events is necessarily equal to $\backslash \; mathcal\; P\; (\backslash \; Omega)$
• Is Ω an unspecified universe; $\backslash \; left\; (\backslash \; Omega,\; \backslash \; \{\backslash \; emptyset,\; \backslash \; Omega\; \backslash \}\; \backslash \; right)$ is a space probabilisable ($\backslash \; \{\backslash \; emptyset,\; \backslash \; Omega\; \backslash \}$ is the coarse tribe).

In practice, the universe Ω is defined according to the random Expérience $\backslash \; mathcal\; E$ carried out, and the tribe is chosen according to the events concerned with the problem.

If we decide to work in the coarse tribe, we will be able to consider only the unquestionable event and the impossible event. When the universe is finished or countable, the discrete tribe is generally chosen: $\backslash \; mathcal\; P\; (\backslash \; Omega)$.

When, on a space probabilisable, one defines a probability, space probabilisable becomes a Espace probabilized.

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