Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-23T19:38:08.667Z Has data issue: false hasContentIssue false
  • English
  • Français

Sets on which Measurable Functions are Determined by their Range

Published online by Cambridge University Press:  20 November 2018

Maxim R. Burke  and
Krzysztof Ciesielski
Maxim R. Burke
Affiliation:
Department of Mathematics and Computer Science, University of Prince Edward Island, Charlottetown, PEI, C1A 4P3
Krzysztof Ciesielski
Affiliation:
Department of Mathematics, West Virginia University, Morgantown, WV 26506-6310, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study sets on which measurable real-valued functions on a measurable space with negligibles are determined by their range.

Keywords

28A2028A0554C0526A3003E3503E50measurable functionmeasurable space with negligiblescontinuous imageset of range uniqueness (SRU)
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 6 , 01 December 1997 , pp. 1089 - 1116
Copyright
Copyright © Canadian Mathematical Society 1997

References

[BS] Bella, A., Simon, S., Function spaces with a dense set of nowhere constant functions. Boll. Un. Mat. Ital. (4A) 7(1990), 121–124.Google Scholar
[BD] Berarducci, A., Dikranjan, D., Uniformly approachable functions and UA spaces. Rend. Istit. Mat. Univ. Trieste 25(1993), 23–56.Google Scholar
[Bü] Büchi, J.R., On the existence of totally heterogeneous spaces. Fund. Math. 41(1954), 97–102.Google Scholar
[BC] Burke, M.R. and Ciesielski, K., Sets of range uniqueness for classes of continuous functions. Submitted.Google Scholar
[CLO] Ciesielski, K., Larson, L., Ostaszewski, K., I-density Continuous Functions. Mem. Amer. Math. Soc. (515) 107(1994).Google Scholar
[CS] Ciesielski, K., Shelah, S., Model with no magic set. Preprint.Google Scholar
[C] Corazza, P., The generalized Borel conjecture and strongly proper orders. Trans. Amer. Math. Soc. 316(1989), 115–140.Google Scholar
[DPR] Diamond, H.G., Pomerance, C., Rubel, L., Sets on which an entire function is determined by its range. Math Z. 176(1981), 383–398.Google Scholar
[DM] Dushnik, B., Miller, E.W., Partially ordered sets. Amer. J.Math. 63(1941), 600–610.Google Scholar
[En] Engelking, R., General Topology, Revised and Completed Edition. Sigma Ser. PureMath. 6, Heldermann Verlag, Berlin, 1989.Google Scholar
[F] Fremlin, D.H., Measure-additive coverings and measurable selectors. Dissertationes Math. 260(1987).Google Scholar
[Je] Jech, T., Set Theory. Academic Press, New York, 1978.Google Scholar
[Ju] Just, W., A modification of Shelah's oracle-cc with applications. Trans. Amer. Math. Soc. 329(1992), 325–356.Google Scholar
[Ku1] Kunen, K., Set Theory. North-Holland Publishing Co., New York, 1983.Google Scholar
[Ku2] Kunen, K., Random and Cohen real. In: Handbook of Set-Theoretic Topologys (Eds. Kunen, K. and Vaughan, J.E.), North-Holland Publishing Co., New York, 1984. 887–911.Google Scholar
[Mi1] Miller, A.W., Some properties of measure and category. Trans. Amer.Math. Soc. 266(1981), 93–114.Google Scholar
[Mi2] Miller, A.W., Special Subsets of the Real Line. In: Handbook of Set-Theoretic Topology (Eds. Kunen, K. and Vaughan, J.E.), North-Holland Publishing Co., New York, 1984. 201–233.Google Scholar
[Mi3] Miller, A.W., Mapping a set of reals onto the reals. J. Symbolic Logic 48(1983), 575–584.Google Scholar
[Ox] Oxtoby, J.C., Measure and Category. Graduate Texts in Math., 2nd edn, Springer-Verlag, New York, 1980.Google Scholar
[Ro] Royden, H.L., Real Analysis. Prentice Hall, 1988.Google Scholar
[Ru] Rudin, W., Real and Complex Analysis. McGraw-Hill, 1987.Google Scholar
[Sh] Shelah, S., Independence results. J. Symbolic Logic 45(1980), 563–573.Google Scholar
[Ta] Tall, F.D., The density topology. Pacific Math. J. (1) 62(1976), 275–284.Google Scholar
[To] Todorcevic, S., Partition problems in topology. Contemp. Math. 84, Amer. Math. Soc., Providence, RI, 1989.Google Scholar