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On Gaussian measures in certain locally convex spaces

  • Mathematics


The main purpose of this paper is threefold: Firstly, the topological support of Gaussian measures on certain locally convex spaces is obtained. Secondly, strongly convergent series expansions of elements in separable Fréchet spaces, related to Gaussian measures, are obtained; this result is applied to obtain Karhunen-Loève-type expansions for Gaussian processes. Thirdly, it is shown that any zero-mean Gaussian measure on a separable Fréchet space can be obtained as the [sigma] extension of the canonical Gaussian cylinder measure of a separable Hilbert space. Other related problems are also discussed.

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