Celebratio Mathematica — Moore — Complete Bibliography

Complete Bibliography

Works connected to Peter Florin Hahn

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J. Feldman, P. Hahn, and C. C. Moore: “Orbit structure and countable sections for actions of continuous groups,” Adv. Math. 28 : 3 (June 1978), pp. 186–230. MR 492061 Zbl 0392.28023 article

It is shown that if a second countable locally compact group \( G \) acts nonsingularly on an analytic measure space \( (S,\mu) \), then there is a Borel subset \( E\subset S \) such that \( EG \) is conull in \( S \) and each \( sG\cap E \) is countable. It follows that the measure groupoid constructed from the equivalence relation \( s\sim sg \) on \( E \) may be simply described in terms of the measure groupoid made from the action of some countable group. Some simplifications are made in Mackey’s theory of measure groupoids. A natural notion of “approximate finiteness” (\( AF \)) is introduced for nonsingular actions of \( G \), and results are developed parallel to those for countable groups; several classes of examples arising naturally are shown to be \( AF \). Results on “skew product” group actions are obtained, generalizing the countable case, and partially answering a question of Mackey. We also show that a group-measure space factor obtained from a continuous group action is isomorphic (as a von Neumann algebra) to one obtained from a discrete group action.

Peter Florin Hahn	Related
Jacob Feldman	Related

J. Feldman, P. Hahn, and C. C. Moore: “Sections for group actions, and some applications,” pp. 167–174 in Algèbres d’opérateurs et leurs applications en physique mathématique [Operator algebras and their applications in mathematical physics] (Marseille, 20–24 June 1977). Edited by A. Connes, D. Kastler, and D. W. Robinson. Colloques Internationaux du Centre National de la Recherche Scientifique 274. CNRS (Paris), 1979. MR 560632 Zbl 0429.28019 incollection

Alain Connes	Related
Jacob Feldman	Related
Peter Florin Hahn	Related
Daniel Kastler	Related
Derek W. Robinson	Related