This preprint was accepted January, 1998
Contact: A.M.Vershik and Yu.V.Yakubovich
ABSTRACT: In this paper we deal with some class of continuous partition lattices, introduced by A. Bjorner in 1987 as a limit of finite partition lattices. We describe the direct way how to construct the continuous partition lattice in terms of measurable partitions of the measure space and present a simple realization of such lattices. Secondly, we give a representation of continuous partition lattice in a factor of type II_1 and in the continuous geometries in the sense of von~Neumann. Thirdly, the continuous hyperfinite partition lattice is used to state and solve one natural asymptotical problem.