Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Liftings of functions with values in a completely regular space
HTML articles powered by AMS MathViewer

by G. A. Edgar and Michel Talagrand PDF
Proc. Amer. Math. Soc. 78 (1980), 345-349 Request permission

Abstract:

Let T be a completely regular space, let $(\Omega ,\mathcal {F},\mu )$ be complete probability space, and let $\rho :{\mathcal {L}^\infty }(\mu ) \to {\mathcal {L}^\infty }(\mu )$ be a lifting. If $f:\Omega \to T$ is a Baire measurable function, must there exist a function $\tilde f$ with almost all of its values in T, such that $\rho (h \circ f) = h \circ \tilde f$ for all bounded continuous functions h on T? If T is strongly measure-compact, then the answer is “yes". If T is not measure-compact, then the answer is “no". This shows that a lifting is not always the best method for the construction of weak densities for vector measures.
References
  • G. A. Edgar, Measurability in a Banach space, Indiana Univ. Math. J. 26 (1977), no. 4, 663–677. MR 487448, DOI 10.1512/iumj.1977.26.26053
  • André Goldman, Mesures cylindriques, mesures vectorielles et questions de concentration cylindrique, Pacific J. Math. 69 (1977), no. 2, 385–413 (French). MR 473135
  • A. Ionescu Tulcea and C. Ionescu Tulcea, Topics in the theory of lifting, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 48, Springer-Verlag New York, Inc., New York, 1969. MR 0276438
  • J. D. Knowles, Measures on topological spaces, Proc. London Math. Soc. (3) 17 (1967), 139–156. MR 204602, DOI 10.1112/plms/s3-17.1.139
    • W. Moran, Measures and mappings on topological spaces, Proc. London Math. Soc. 19 (1969), 493-508.
  • Kazimierz Musiał, The weak Radon-Nikodým property in Banach spaces, Studia Math. 64 (1979), no. 2, 151–173. MR 537118, DOI 10.4064/sm-64-2-151-174
  • John C. Oxtoby, Measure and category. A survey of the analogies between topological and measure spaces, Graduate Texts in Mathematics, Vol. 2, Springer-Verlag, New York-Berlin, 1971. MR 0393403
  • Christian Sunyach, Une caractérisation des espaces universellement Radon-mesurables, C. R. Acad. Sci. Paris Sér. A-B 268 (1969), A864–A866 (French). MR 248321
    • V. S. Varadarajan, Measures on topological spaces, Amer. Math. Soc. Transl. (2) 48 (1965), 161-228.
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46G15, 28A51
  • Retrieve articles in all journals with MSC: 46G15, 28A51
Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 78 (1980), 345-349
  • MSC: Primary 46G15; Secondary 28A51
  • DOI: https://doi.org/10.1090/S0002-9939-1980-0553373-0
  • MathSciNet review: 553373