Abstract
This article deals with measurablemultilinear mappings on Frechet spaces and analogs of two properties which are equivalent for a measurable (with respect to gaussian measure) linear functional: (i) there exists a sequence of continuous linear functions converging to the functional almost everywhere; (ii) there exists a compactly embedded Banach space X of full measure such that the functional is continuous on it. We show that these properties for multilinear functions defined on a power of the space X are not equivalent; but property (ii) is equivalent to the apparently stronger condition that the compactly embedded subspace is a power of the subspace embedded in X.
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