Charakteristische Funktionale zuf�lliger Ma\e

Abstract

The principal aim of the paper is an analogue of Levy's theorem in the following way: Let \(\mathfrak{X}\) be a locally compact space denumerable in the infinity and consider the space \(\mathfrak{M}(\mathfrak{X})\) of all positive Radon measures on \(\mathfrak{X}\) with the “topologie vague” in the sense of Bourbaki. The Fouriertransform of a tight measure P on \(\mathfrak{M}(\mathfrak{X})\) is the functional $$\varphi \varepsilon \mathfrak{L}(\mathfrak{X}) \to \hat P(\varphi ) = \int {P(\mu ){\text{ }}\exp i\langle \mu ,\varphi \rangle } $$ where \(\mathfrak{L}(\mathfrak{X})\) is the space of all continuous functions with compact support.