Yehuda Shalom

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Let k be any locally compact non-discrete field. We show that finite invariant measures for k-algebraic actions are obtained only via actions of compact groups. This extends both Borel’s density and fixed point theorems over local fields (for semisimple/solvable groups, resp.). We then prove that for k-algebraic actions, finitely additive finite invariant(More)
6. Principal bundles, induction, and cohomology I. Principal bundles and induction of unitary representations II. A " transference " theorem III. The bundle-induction operation on the first cohomology 1. Introduction and discussion of the main results I. Introduction. Throughout the last two or three decades, the theory of rigidity, particularly in relation(More)
The Margulis-Zimmer conjecture. The subject of this paper is a well known question advertised by Gregory Margulis and Robert Zimmer since the late 1970’s, which seeks refinement of the celebrated Normal Subgroup Theorem of Margulis (hereafter abbreviated NST). Although Margulis’ NST is stated and proved in the context of (higher rank) irreducible lattices(More)
Let G be a group generated by a finite subset S; define S to be the set Ž . < n < of all products of at most n elements of S, and let a S s S be the n n Ž . Ž . Ž . Ž . number of elements in S . As a S satisfies 1 F a S F a S ? a S , n nqm n m Ž .1r n Ž . Ž .1r n the limit lim a S exists, and a S s lim a S G 1. Although the n n Ž . exact value of a S(More)
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