Measures on infinite-dimensional orthomodular spaces

We classify the measures on the lattice of all closed subspaces of infinite-dimensional orthomodular spaces (E, ) over fields of generalized power series with coefficients in . We prove that every -additive measure on can be obtained by lifting measures from the residual spaces of (E, ). The measures being lifted are known, for the residual spaces are Euclidean. From the classification we deduce, among other things, that the set of all measures on is not separating.Research supported by the Swiss National Science Foundation.