A function P: F → [0,1] with P(Ω) = 1 and countable additivity (P(⋃ Aᵢ) = ΣP(Aᵢ) for pairwise disjoint events). Kolmogorov's 1933 axiomatisation of probability.
Probability measure P
Related concepts
- σ-algebra F
- Conditional probability
- Expectation E[X]
- Maximum-likelihood estimation
- Lebesgue measure
- Statistical hypothesis testing
- Bayesian inference
- Random graph (Erdős–Rényi)
- Weak convergence of measures
- Probabilistic method (Erdős)
- Monte Carlo integration
- Stochastic gradient descent
- Maximum likelihood estimation
- Measure-preserving transformation
- Borel-Cantelli lemmas
- Kolmogorov's zero-one law
- Born rule
- Boltzmann entropy formula
- Maxwell-Boltzmann distribution
- Galactic cosmic rays (GCRs)