Vague Topology
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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) .…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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) .