Probability theory and stochastic processes Concept
Probability measure
Summary
A probability measure is a countably additive function on a σ-algebra of events that gives the whole space the value . It assigns to each event its probability. The node probability measure gives the precise definition.
Where this leads
68 pages build on this one.
- Concentration of measure
- Krylov–Bogolyubov theorem
- Self-similar measure
- Ergodic decomposition
- Jordan–Kinderlehrer–Otto scheme
- Benamou–Brenier formula
- Ratner's theorems
- Bilateral Laplace transform of a probability law
- XYZ inequality
- Percolation theory
- Portmanteau theorem
- Finite measure
- Evans potential theorem
- Contiguity of measures
- Kiefer–Wolfowitz equivalence theorem
- Capacity and Hausdorff dimension
- Ionescu-Tulcea theorem
- Tightness of measures
- Borel–Kolmogorov paradox
- Logarithmic capacity
- Regular conditional probability
- Kantorovich duality
- Dynkin's π-λ theorem
- Varadhan's lemma
- Random walk on a group
- Robust statistics
- Brenier's theorem
- Prokhorov's theorem
- FKG inequality
- Infinite product measure
- Erdős–Rényi model
- Equilibrium measure
- Variational principle for topological entropy
- Young measure
- Skorokhod's representation theorem
- Weak convergence of measures
- Optimal transport and the Monge problem
- Unique ergodicity
- Gibbs measure
- Poisson boundary
- Large deviations theory
- Disintegration theorem
- Gaussian measure
- Choquet theory
- Displacement convexity
- Total variation distance between probability measures
- Lévy–Khintchine representation
- Sanov's theorem
- Cylinder set measure
- Wasserstein metric
- Analyticity of the bilateral Laplace transform of a law
- Cramér's theorem
- Minlos theorem
- Relaxed control
- Kantorovich–Rubinstein duality
- Lévy–Prokhorov metric
- Coupling
- Markov kernel
- De Finetti's theorem
- Harris inequality
- Kolmogorov extension theorem
- Kullback–Leibler divergence
- Skorokhod's embedding theorem
- Equilibrium problem with an external field
- Hellinger distance
- Robin constant
- Abstract Wiener space
- Girsanov theorem
Further reading
- Web https://en.wikipedia.org/wiki/Probability_measure, lead section
About this page
| Tag | 059TJN0NZ1 |
|---|---|
| URI | m2://059TJN0NZ1 |
| Aliases | probability-function |
| Kind | concept |
| Writing | W1 stated |
| MSC | 60A10 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (1 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
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What links here
Special cases
Definitions
Used by
- Concentration of measure
- Krylov–Bogolyubov theorem
- Self-similar measure
- Ergodic decomposition
- Jordan–Kinderlehrer–Otto scheme
- Benamou–Brenier formula
- Ratner's theorems
- Bilateral Laplace transform of a probability law
- Percolation theory
- Portmanteau theorem
- Finite measure
- Evans potential theorem
- Contiguity of measures
- Kiefer–Wolfowitz equivalence theorem
- Capacity and Hausdorff dimension
- Ionescu-Tulcea theorem
- Tightness of measures
- Borel–Kolmogorov paradox
- Logarithmic capacity
- Regular conditional probability
- Kantorovich duality
- Dynkin's π-λ theorem
- Varadhan's lemma
- Random walk on a group
- Prokhorov's theorem
- Infinite product measure
- Erdős–Rényi model
- Equilibrium measure
- Variational principle for topological entropy
- Young measure
- Skorokhod's representation theorem
- Weak convergence of measures
- Optimal transport and the Monge problem
- Unique ergodicity
- Gibbs measure
- Poisson boundary
- Large deviations theory
- Disintegration theorem
- Gaussian measure
- Choquet theory
- Total variation distance between probability measures
- Lévy–Khintchine representation
- Sanov's theorem
- Cylinder set measure
- Wasserstein metric
- Analyticity of the bilateral Laplace transform of a law
- Minlos theorem
- Relaxed control
- Kantorovich–Rubinstein duality
- Lévy–Prokhorov metric
- Coupling
- Markov kernel
- De Finetti's theorem
- Harris inequality
- Kolmogorov extension theorem
- Kullback–Leibler divergence
- Skorokhod's embedding theorem
- Equilibrium problem with an external field
- Hellinger distance
- Robin constant
- Abstract Wiener space
- Girsanov theorem
Results about this
- Ionescu-Tulcea theorem
- Optimal transport and the Monge problem
- Disintegration theorem
- Kolmogorov extension theorem