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Let $\mu$ be a Gaussian measure on some measurable space$\{W=\{w\},{\mathcal{B}}(W)\}$ and let $\nu$ be a measure on the same spacewhich is absolutely continuous with respect to $\nu$. The paper surveys resultson the problem of constructing a transformation $T$ on the $W$ space such that$Tw=w+u(w)$ where $u$ takes values in the Cameron-Martin space and the image of$\mu$ under $T$ is $\mu$. In addition we ask for the existence oftransformations $T$ belonging to some particular classes.

The realization of positive random variables via absolutely continuous transformations of measure on Wiener space