Let (Ω,,P) be a probability space and let τ: ℝ×Ω → ℝ be a function which is strictly increasing and continuous with respect to the first variable, measurable with respect to the second variable. Given the set of all continuous probability distribution solutions of the equation $F\left(x\right)={\int }_{\Omega }F\left(\tau (x,\omega )\right)dP\left(\omega \right)$ we determine the set of all its probability distribution solutions.