Probabilities on first order models

It is known that set algebras corresponding to first order models (i.e., cylindric set algebras associated with first order interpretations) are not æ-closed, but closed w.r.t. certain infima and suprema i.e., (⁄) j9xfij = i2! jfi(yi)j and j8xfij = i2! jfi(yi)j for any infinite subsequence y1;y2;:::yi;::: of the individuum variables in the language. We investigate probabilities defined on these set algebras and being continuous w.r.t. the suprema and infima in (⁄). We can not use the usual technics, because these suprema and infima are not the usual unions and inter- sections of sets. These probabilities are interesting in computer science among others, because the probabilities of the quantifier-free formulas determine that of any formula, and the probabilities of the former ones can be measured by statistical methods.