Probability space

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Sample space, event, outcome

Definition: Sample space

A sample space S is just a set. We refer to the elements of S as outcomes. We refer to the subsets of S as events.

Probability measure, Kolmogorov's axioms

Definition: probability measure

A probability measure on a sample space S is a function satisfying the following three properties:

For all events [math]E [/math],
For all disjoint events [math]E_1 [/math] and [math]E_2 [/math],

These three properties are referred to as the Kolmogorov axioms.

Probability space

Definition: Probability space

A probability space is just a pair containing a sample space S and a probability measure on S.

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