We consider sufficient conditions for the absolute continuity of the distribution of a smooth function f on an infinite-dimensional space X equipped with a measure μ. We shall assume that X is a locally convex space and μ is a Radon probability measure on X (see [1]). Various conditions of this sort are known for many classes of functions and measures, see [2-9]. An important sufficient condition is known in the onedimensional case where the following simple fact is true: if μ is an absolutely continuous measure and f is an arbitrary function, then, letting D be the set where f has a nonzero derivative, we obtain that the restriction of μ to D is taken by f to an absolutely continuous measure, i.e., the measure μ|_D ° f~(-1) is absolutely continuous (it is known that in the considered case the set D is always Lebesgue measurable and f is measurable on D). The results obtained answer a question posed by S.B. Kuksin and are used in the recent paper [10].
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