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- Vague_topology abstract "In mathematics, particularly in the area of functional analysis and topological vector spaces, the vague topology is an example of the weak-* topology which arises in the study of measures on locally compact Hausdorff spaces.Let X be a locally compact Hausdorff space. Let M(X) be the space of complex Radon measures on X, and C0(X)* denote the dual of C0(X), the Banach space of complex continuous functions on X vanishing at infinity equipped with the uniform norm. By the Riesz representation theorem M(X) is isometric to C0(X)*. The isometry maps a measure μ to a linear functionalThe vague topology is the weak-* topology on C0(X)*. The corresponding topology on M(X) induced by the isometry from C0(X)* is also called the vague topology on M(X). Thus, in particular, one may refer to vague convergence of measure μn → μ.One application of this is to probability theory: for example, the central limit theorem is essentially a statement that if μn are the probability measures for certain sums of independent random variables, then μn converge weakly to a normal distribution, i.e. the measure μn is "approximately normal" for large n.".
- Vague_topology wikiPageID "15393951".
- Vague_topology wikiPageRevisionID "487285004".
- Vague_topology hasPhotoCollection Vague_topology.
- Vague_topology id "7212".
- Vague_topology title "Weak-* topology of the space of Radon measures".
- Vague_topology subject Category:Real_analysis.
- Vague_topology subject Category:Topology_of_function_spaces.
- Vague_topology comment "In mathematics, particularly in the area of functional analysis and topological vector spaces, the vague topology is an example of the weak-* topology which arises in the study of measures on locally compact Hausdorff spaces.Let X be a locally compact Hausdorff space. Let M(X) be the space of complex Radon measures on X, and C0(X)* denote the dual of C0(X), the Banach space of complex continuous functions on X vanishing at infinity equipped with the uniform norm.".
- Vague_topology label "Vague topology".
- Vague_topology sameAs m.03m6yw6.
- Vague_topology sameAs Q17125297.
- Vague_topology sameAs Q17125297.
- Vague_topology wasDerivedFrom Vague_topology?oldid=487285004.
- Vague_topology isPrimaryTopicOf Vague_topology.