This paper deals with rate distortion or source coding with fidelity criterion, in measure spaces, for a class of source distributions. The class of source distributions is described by a relative entropy constraint set between the true and a nominal distribution. The rate distortion problem for the class is thus formulated and solved using minimax strategies, which result in robust source coding with fidelity criterion. It is shown that minimax and maxmin strategies can be computed explicitly, and they are generalizations of the classical solution. Finally, for discrete memoryless uncertain sources, the rate distortion theorem is stated for the class omitting the derivations while the converse is derived.