[[Actuarial Notes Wiki|Wiki]] / [[Actuarial Math]] / [[Probability Theory]] / ==Foundational Mathematics of Probability== > The mathematical definition of probability depends on [[Measure Theory]]. Probability is a measure, or a mapping from an event space to the real numbers. | Name | Definition | | ----------------------- | ------------------------------------------------------------ | | **Probability Space** | A measure space (Ω, ∑, p) with the requirement that p(Ω) = 1 | | Sample Space (Ω) | The set of all possible outcomes of a random experiment. | | Event Space (∑) | A sigma-algebra over Ω | | Probability Measure (p) | A measure p : Ω → R ∪ {∞} |