A Characterization of Bimeasurable Functions in Terms of Universally Measurable Sets

The purpose of this note is to show, assuming the continuum hypothesis, that a Borel function, /, mapping a Borel subset, Df, of a separable complete metric space, Mi, into a separable complete metric space, Mi, maps Borel subsets of Df onto Borel subsets of M if, and only if, / maps universally measurable subsets of Df onto universally measurable subsets of Mi.