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The group of measure-preserving transformations of closed unit interval has no outer automorphism. (English) Zbl 0465.28008


MSC:

28D15 General groups of measure-preserving transformations
28A60 Measures on Boolean rings, measure algebras
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References:

[1] Choksi, J.R., Prasad, V.S.: Ergodic theory on homogeneous measure algebras (to appear, in Measure Theory, Oberwolfach, 1981) · Zbl 0497.28008
[2] Dye, H.A.: On groups of measure preserving transformations. II. Am. J. Math.85, 551-576 (1963) · Zbl 0191.42803 · doi:10.2307/2373108
[3] Fathi, A.: Le groupe des transformations de [0, 1] qui preservent la mesure de Lebesgue est un groupe simple. Israel J. Math.29, 302-308 (1978) · Zbl 0375.28008 · doi:10.1007/BF02762017
[4] Halmos, P.R.: Approximation theories for measure-preserving transformations. Trans. A.M.S.55, 1-18 (1944) · Zbl 0063.01890
[5] Halmos, P.R., von Neumann, J.: Operator methods in classical mechanics. II. Ann. Math.43, 332-350 (1942) · Zbl 0063.01888 · doi:10.2307/1968872
[6] Maharam, D.: On homogeneous measure algebras. Proc. N.A.S.28, 108-111 (1942) · Zbl 0063.03723 · doi:10.1073/pnas.28.3.108
[7] Maharam, D.: Automorphisms of products of measure spaces. Proc. A.M.S.9, 702-707 (1958) · Zbl 0102.04102 · doi:10.1090/S0002-9939-1958-0097494-6
[8] Royden, H.L.: Real analysis. New York: Macmillan 1968 · Zbl 0197.03501
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