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Linear liftings for non-complete probability spaces

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Abstract

We show that it is consistent with ZFC thatL ∞(Y,B,ν) has no linear lifting for many non-complete probability spaces (Y,B,ν), in particular forY=[0,1]A,B=Borel subsets ofY, ν=usual Radon measure onB.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Prince Edward Island, C1A 4P3, Charlottetown, Prince Edward Island, Canada

    Maxim R. Burke

  2. Institute of Mathematics, The Hebrew University, Jerusalem, Israel

    Saharon Shelah

Authors
  1. Maxim R. Burke
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  2. Saharon Shelah
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Additional information

Research supported by UPEI Senate Grant no 602101, by the Research Institute for Mathematical Sciences at Bar-Ilan University, and by the Landau Center for Mathematical Research in Analysis (supported by the Minerva Foundation). The author would like to thank the organizers of the Winter Institute on the Set Theory of the Reals for their hospitality while part of this research was being carried out.

Partially supported by the Foundation for Basic Research of the Israel Academy of Science. Publication number 437.

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Burke, M.R., Shelah, S. Linear liftings for non-complete probability spaces. Israel J. Math. 79, 289–296 (1992). https://doi.org/10.1007/BF02808221

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  • DOI: https://doi.org/10.1007/BF02808221

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