On Measurability over Product Spaces

The main result announced here is a negative solution of the Kakutani-Doob problem [3 ] on measurability of stochastic processes, assuming the continuum hypothesis. Thus the positive solution proposed earlier by M. Mahowald [ó] is incorrect (the last step in the argument applies the Fubini theorem to sets in a product space which need not be measurable). Complete proofs will appear in the Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability. Preprints are available from the author. The problem can be formulated as follows. Let