Abstract
We generalize the result of Hamhalter and Ptak showing that an inner product space whose dimension is either a nonmeasurable cardinal or an arbitrary cardinal is complete iff its lattice of strongly closed subspaces possesses at least one state or one completely additive state, respectively. Moreover, we show that this lattice of any separable space possesses manyσ-finite measures, and we give the Gleason analogue for them.
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