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**Parent**: Probability

A probability space is a 3-tuple (\Omega, F, P) consisting of

- A set \(\Omega\) called the sample space i.e. the set of all possible outcomes
- A \(\sigma\)-algebra \(F\) on the set \(\Omega\), which informally specifies the set of all “possible” events (events are outcomes or combinations of outcomes)
- A probability measure \(P: F \rightarrow [0, 1]\)

The 2-tuple \((\Omega, F)\) is called a **measure space**.

A **measurable space** (also called a Borel space) is a 2-tuple consisting of

- A set \(X\)
- A A \(\sigma\)-algebra on the set \(X\)

When the 2-tuple measure space is equipped with a measure \(\mu\), becoming a 3-tuple,
the measurable space becomes a **measure space**.