A note on measurability and almost continuity

Burke, Maxim R.; Fremlin, David H.

doi:10.1090/S0002-9939-1988-0928989-7

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.

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A note on measurability and almost continuity
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by Maxim R. Burke and David H. Fremlin PDF

Proc. Amer. Math. Soc. 102 (1988), 611-612 Request permission

Abstract:

We prove that it is consistent with ZFC that there exist a measurable function $f:\left [ {0,1} \right ] \to {\omega _1}$ which is not almost continuous.

References

Kenneth Kunen and Jerry E. Vaughan (eds.), Handbook of set-theoretic topology, North-Holland Publishing Co., Amsterdam, 1984. MR 776619
D. H. Fremlin, Measurable functions and almost continuous functions, Manuscripta Math. 33 (1980/81), no. 3-4, 387–405. MR 612620, DOI 10.1007/BF01798235