Gleason Measures

Offprint from Probabilistic Analysis and Related Topics, Vol. 2. Academic Press, Inc., 1979, pp. 69-103. Original self-wrappers, stapled as issued; clean. A publisher's offprint of a substantial survey article presenting a systematic and largely self-contained account of the theory of measures on the lattice of all closed subspaces of a Hilbert space, grounded in Gleason's classical theorem on the general form of positive finite measures on the lattice Proj H of orthogonal projectors in a separable Hilbert space. The eight sections cover: introduction; generalities; orthogonally scattered Gleason measures; L₂,s(H)-spaces and isometries generated by OSG measures; spectral Gleason measures; convergence of Gleason measures; Gleason measures in tensor products; and random Gleason measures -- with many results described as appearing here for the first time.