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We study Gaussian random fields on certain Banach spaces and investigateconditions for their existence. Our results apply inter alia to spaces of Radonmeasures and H\"older functions. In the former case, we are able to defineGaussian white noise on the space of measures directly, avoiding, e.g., anembedding into a negative-order Sobolev space. In the latter case, wedemonstrate how H\"older regularity of the samples is controlled by that of thecovariance kernel and, thus, show a connection to the Theorem ofKolmogorov-Chentsov.

Gaussian random fields on non-separable Banach spaces