Let X be a random variable with a differentiable disribution function F, let (a,b) denote the unique interval such that \(0<F(x)<1\) for \(a<x<b\) and \(F(x)=1\) or 0 for \(x\not\in (a,b)\), and, for \(a<x<b\), define \[ K_{\alpha}(x)=E(F^{-\alpha}(X)| X<x). \] The author shows that the function \(K_{\alpha}\) uniquely determines the distribution of X via the formula \[ F(x)=(l-\alpha)^{\alpha}K^{\alpha}_{\alpha}(x),\quad a<x<b. \]