THE EXCHANGE PROPERTY AND THE ENDS OF OPT IONAL SETS

For the characterization of the Brownian filtration it would be conven ient according to M. Barlow [2] to determine the sigma-algebra F-L+ of the ''germinative'' past at the instant L in terms of the sigma-algeb ra F-L of the past at the instant L. in this determination, essentiall y two problems appear: on one hand the exchange between the supremum a nd the intersection of a decreasing sequence of sigma-fields, on the o ther hand the evaluation of the germ sigma-field. This paper, by means of V. Weiszacker's criterium [5], solves completely the first problem , at the price of a slight modification of the notion of the germ sigm a-field.