measure-theoretic construction
C11644
concept
A measure-theoretic construction is a rigorous method of building mathematical objects—such as measures, integrals, or probability spaces—by specifying σ-algebras, set functions, and limiting processes that satisfy the axioms of measure theory.
All labels observed (11)
| Label | Occurrences |
|---|---|
| result in measure theory | 7 |
| Borel measure | 2 |
| construction in ergodic theory | 2 |
| construction in functional analysis | 2 |
| measure in harmonic analysis | 2 |
| outer measure | 2 |
| complete measure | 1 |
| construction in stochastic calculus | 1 |
| increasing family of sigma-algebras | 1 |
| measure-theoretic construction canonical | 1 |
| stochastic process measure | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: measure-theoretic construction
Generated description
A measure-theoretic construction is a rigorous method of building mathematical objects—such as measures, integrals, or probability spaces—by specifying σ-algebras, set functions, and limiting processes that satisfy the axioms of measure theory.
Instances (20)
| Instance | Via concept surface |
|---|---|
| Carathéodory’s extension theorem | result in measure theory |
| Gelfand transform | construction in functional analysis |
| monotone convergence theorem | result in measure theory |
| Lebesgue measure | complete measure |
| Brownian filtration | increasing family of sigma-algebras |
| Wiener measure | stochastic process measure |
| Kolmogorov extension theorem | result in measure theory |
| Itô integral | construction in stochastic calculus |
| Steinhaus theorem | result in measure theory |
| Lebesgue differentiation theorem | result in measure theory |
| Vitali covering lemma | result in measure theory |
| Hahn decomposition theorem | result in measure theory |
| Lebesgue integration | — |
| Hausdorff measure | outer measure |
| Kakutani skyscraper construction | construction in ergodic theory |
| Kakutani–Rokhlin towers | construction in ergodic theory |
| Plancherel measure | measure in harmonic analysis |
| Stieltjes measure | Borel measure |
| Gelfand–Naimark–Segal construction | construction in functional analysis |
| Carleson measure | measure in harmonic analysis |