Absolute continuity of the images of measures (Q1822410)

Let (X,\({\mathcal S},\mu)\) be a finite measure space, \(f: X\to {\mathbb{R}}^ a \)measurable mapping. Conditions under which the image \(\mu \circ f^{- 1}\) is absolutely continuous (with respect to the Lebesgue measure) are studied. Special attention is paid to the case when \(\mu\) is the distribution of a random function and X it's sample path space.