Appendix A

Probability Review

A.1 Standard Probability Theory

A.1.1 Probability Space

A probability space (Ω, bapp01-math-0001, ) is the provision of:

  • A set of all possible outcomes ω ∈ Ω, sometimes called states of Nature
  • A σ-algebra, that is, a set of measurable events Abapp01-math-0002, which (1) contains ∅, (2) is stable by complementation (bapp01-math-0003) and (3) is stable by countable unions (bapp01-math-0004)
  • A probability measure : bapp01-math-0005 → [0, 1], which (1) satisfies (Ω) = 1 and (2) is countably additive (bapp01-math-0006 where denotes disjoint union)

A.1.2 ...

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