ON THE EXISTENCE OF PRODUCT STOCHASTIC MEASURES

In this paper, we prove that the existence of product stochastic measures depends on the axiomsystem of set theory: If one aecepts the axiom of choice, the answer is negative, and we give acounter-example where the product stochastic measure doesn’t exist; but in the Solovay model (onekind of set theory which refuses the axiom of choice),the answer is positive, and we give a proof.