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