  We show that the following five categories are equivalent: (1) the opposite
category of commutative von Neumann algebras; (2) compact strictly localizable
enhanced measurable spaces; (3) measurable locales; (4) hyperstonean locales;
(5) hyperstonean spaces. This result can be seen as a measure-theoretic
counterpart of the Gelfand duality between commutative unital C*-algebras and
compact Hausdorff topological spaces.
