Probability space

• “A Probability space is a Measure space such that the Measure of the whole space is equal to one.”

• “A Probability space is a triple (Ω,F,P) consisting of:

  • the sample space Ω : set α — an arbitrary non-empty set,

  • the σ-algebra F ⊆ 2^Ω — a set of subsets of Ω, called events, such that:

    • Ω ∈ F;

    • F is closed under complements: A ∈ F → (Ω∖A) ∈ F;

    • F is closed under countable unions: A i ∈ F → (⋃ i, A i) ∈ F;

  • the Probability measure P.”

References

• Wikipedia;

• Mathlib;