Statements (59)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
σ-algebra
|
| gptkbp:contains |
countable unions of open sets
all closed sets all open sets countable intersections of open sets |
| https://www.w3.org/2000/01/rdf-schema#label |
Borel σ-algebra
|
| gptkbp:isA |
σ-algebra of subsets
|
| gptkbp:isAccessibleBy |
open intervals
|
| gptkbp:isDescribedAs |
topological space
|
| gptkbp:isEquippedWith |
with respect to a measure
|
| gptkbp:isLocatedIn |
complementation
countable intersections countable operations countable unions complement_of_Borel_sets countable_intersections_of_Borel_sets countable_unions_of_Borel_sets |
| gptkbp:isMaintainedBy |
open sets
Borel_sets |
| gptkbp:isNamedAfter |
gptkb:Émile_Borel
|
| gptkbp:isRelatedTo |
gptkb:Borel_hierarchy
topology Lebesgue measure real analysis measurable spaces Borel sigma-algebra on R Borel_functions Borel_isomorphism Borel_measurable_space Borel_sets_in_metric_spaces |
| gptkbp:isUsedBy |
Borel probability measures
Borel_measurable_functions |
| gptkbp:isUsedIn |
theoretical computer science
information theory topological groups probability theory differential equations statistical mechanics functional analysis game theory numerical analysis functional equations measure theory probability distributions statistical inference stochastic processes complex analysis dynamical systems Lebesgue integration ergodic theory applied mathematics random processes nonlinear analysis real-valued random variables topological vector spaces measure-theoretic probability functional limit theorems measure-theoretic topology quantum_mechanics |