Vague topology

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 functional

单词	Vague topology
释义	Vague topology 英语百科 Vague topology 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 functional
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