CHANGE OF MEASURES AND THEIR LOGARITHMIC DERIVATIVES UNDER SMOOTH TRANSFORMATIONS

The main result of this Note is the general Girsanov-Ramer type formul a (1). Here nu is a measure on a locally convex space E with a logarit hmic derivative beta(nu) : H x E --> R of nu with respect to a Hilbert space H subset of E. For the vector field h : E --> H we suppose that there is a sufficiently smooth map F : R x E --> E such that F(0, x) = x et F(1, x) = x + h(x). Under these assumptions(1) holds where U-h( nu) is given by (2) where f(1)' is the partial derivative of F with re spect to t.