Some results on logarithmic derivatives of measures on a locally convex space (Q1896989)

Let \(\mu\) be a \(\sigma\)-additive real-valued measure on the \(\sigma\)-algebra of Borel subsets of a locally convex linear space \(X\). For \(h\in X\), a real-valued function \(\beta_\mu(h,\cdot)\) is the logarithmic derivative of \(\mu\) in the direction \(h\) if for each real-valued bounded ``smooth'' function on \(X\) holds \[ \int f'(x)h\mu(dx)=- \int f(x) \beta_\mu(h, x)\mu(dx). \] The author studies the problem of restoration of the measure \(\mu\) from its logarithmic derivative.