Measure and integration Measures on topological spaces Concept
Radon measure
Summary
A Radon measure on a Hausdorff topological space is a Borel measure that is locally finite and inner regular with respect to compact sets. Radon measures are the measures that fit well with the topology. On a locally compact Hausdorff space, the Riesz–Markov–Kakutani theorem represents each positive linear functional on continuous functions of compact support by such a measure. Lebesgue measure, Haar measures and the usual measures of probability on Polish spaces are Radon measures.
Where this leads
20 pages build on this one.
- Fukushima correspondence between Dirichlet forms and processes
- Domination principle
- Capacity and Hausdorff dimension
- Lattice in a locally compact group
- Haar measure
- De Giorgi's structure theorem
- Riesz–Markov–Kakutani representation theorem
- Heat potential
- Maximum principle for potentials
- Beurling–Deny formula
- Riesz measure of a subharmonic function
- Frostman lemma
- Continuity principle
- Existence and uniqueness of Haar measure
- Modular function
- Mean-periodic function
- Caccioppoli set
- Wolff potential
- Varifold
- Bochner's theorem
Further reading
About this page
| Tag | HZNEQQBCW4 |
|---|---|
| URI | m2://HZNEQQBCW4 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 28C15, 28C05 |
| Specializes | Locally finite measure, Inner regular measure |
| Same as |
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Used by
- Fukushima correspondence between Dirichlet forms and processes
- Domination principle
- Lattice in a locally compact group
- Haar measure
- De Giorgi's structure theorem
- Riesz–Markov–Kakutani representation theorem
- Heat potential
- Maximum principle for potentials
- Beurling–Deny formula
- Riesz measure of a subharmonic function
- Frostman lemma
- Continuity principle
- Existence and uniqueness of Haar measure
- Mean-periodic function
- Caccioppoli set
- Wolff potential
- Varifold
- Bochner's theorem