Approximation by measure-preserving homeomorphisms

  • John C. Oxtoby
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 318)


Straight Line Segment Bryn Mawr Measurable Transformation Compact Metrizable Space Finite Borel Measure 
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  1. [1]
    Antoine, L., Sur l'homéomorphie de deux figures et de leurs voisinages, J. Math. Pures Appl. (8) 4, 221–325 (1921).Google Scholar
  2. [2]
    Doyle, P. H. and Hocking, J. G., A decomposition theorem for n-dimensional manifolds, Proc. Amer. Math. Soc. 13, 469–471 (1962).MathSciNetzbMATHGoogle Scholar
  3. [3]
    Halmos, P. R., Lectures on ergodic theory, Chelsea, New York, 1956.zbMATHGoogle Scholar
  4. [4]
    Katok, A. B. and Stepin, A. M., Metric properties of measure preserving homeomorphisms (Russian), Uspehi Mat. Nauk 25, no. 2 (151), 193–220 (1970) (Russian Math. Surveys 25, 191–220 (1970)).MathSciNetzbMATHGoogle Scholar
  5. [5]
    Keldyš, L. V., Topological imbeddings in Euclidean space, Proc. Steklov Inst. Math. No. 81 (1966) (translation Amer. Math. Soc. 1968).Google Scholar
  6. [6]
    Neumann, J. v., Einige Sätze über messbare Abbildungen, Ann. of Math. (2) 33, 574–586 (1932).MathSciNetCrossRefGoogle Scholar
  7. [7]
    Oxtoby, J. C., Homeomorphic measures in metric spaces, Proc. Amer. Math. Soc. 24, 419–423 (1970).MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    Oxtoby, J. C. and Ulam, S. M., On the equivalence of any set of first category to a set of measure zero, Fund. Math. 31, 201–206 (1938).Google Scholar
  9. [9]
    Oxtoby, J. C. and Ulam, S. M., Measure-preserving homeomorphisms and metrical transitivity, Ann. of Math. (2), 42, 874–920 (1941).MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • John C. Oxtoby
    • 1
  1. 1.Bryn Mawr CollegeUSA

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