  For a maximal abelian subalgebra $A\subset M$ in a finite von Neumann
algebra, we consider an invariant due to Takesaki which is an equivalence
relation on a standard probability space. We give several characterization of
this invariant and show that it can be reconstructed from the A-bimodule
structure of the GNS Hilbert space $L^2(M)$. In particular, we show that this
invariant is induced by the action of the normalizer on A. Hence, this gives a
new proof to a question of Takesaki.
