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locally finite measure

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  • Locally finite measure — In mathematics, a locally finite measure is a measure for which every point of the measure space has a neighbourhood of finite measure.DefinitionLet ( X , T ) be a Hausdorff topological space and let Sigma; be a sigma; algebra on X that contains… …   Wikipedia

  • Locally finite — The term locally finite has a number of different meanings in mathematics:*Locally finite collection of sets in a topological space *Locally finite group *Locally finite measure *Locally finite poset …   Wikipedia

  • Σ-finite measure — In mathematics, a positive (or signed) measure mu; defined on a sigma; algebra Sigma; of subsets of a set X is called finite, if mu;( X ) is a finite real number (rather than ∞). The measure mu; is called σ finite, if X is the countable union of… …   Wikipedia

  • Measure (mathematics) — Informally, a measure has the property of being monotone in the sense that if A is a subset of B, the measure of A is less than or equal to the measure of B. Furthermore, the measure of the empty set is required to be 0. In mathematical analysis …   Wikipedia

  • Locally convex topological vector space — In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces (TVS) which generalize normed spaces. They can be defined as topological vector… …   Wikipedia

  • Trivial measure — In mathematics, specifically in measure theory, the trivial measure on any measurable space ( X , Σ) is the measure μ which assigns zero measure to every measurable set: μ ( A ) = 0 for all A in Σ.Properties of the trivial measureLet μ denote the …   Wikipedia

  • Dirac measure — In mathematics, a Dirac measure is a measure δx on a set X (with any σ algebra of subsets of X) defined by for a given and any (measurable) set A ⊆ X. The Dirac measure is a probability measure, and in terms of probability it represents …   Wikipedia

  • Locally compact group — In mathematics, a locally compact group is a topological group G which is locally compact as a topological space. Locally compact groups are important because they have a natural measure called the Haar measure. This allows one to define… …   Wikipedia

  • Locally compact space — In topology and related branches of mathematics, a topological space is called locally compact if, roughly speaking, each small portion of the space looks like a small portion of a compact space.Formal definitionLet X be a topological space. The… …   Wikipedia

  • Finite strain theory — Continuum mechanics …   Wikipedia

  • Locally integrable function — In mathematics, a locally integrable function is a function which is integrable on any compact set of its domain of definition. Formal definition Formally, let Omega be an open set in the Euclidean space scriptstylemathbb{R}^n and scriptstyle… …   Wikipedia

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