Masas and Bimodule Decompositions of II₁ Factors

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The measure-multiplicity-invariant for masas in II₁ factors was introduced in MR2261688 to distinguish masas that have the same Pukánszky invariant. In this paper we study the measure class in the measure-multiplicity-invariant. This is equivalent to studying the standard Hilbert space as an associated bimodule. We characterize the type of any masa depending on the left-right-measure using Baire category methods (selection principle of Jankov and von Neumann). We present a second proof of Chifan's result on normalisers and a measure theoretic proof of the equivalence of weak asymptotic homomorphism property (WAHP) and singularity that appeared in MR2417416.