Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Some undecidability results concerning Radon measures

Authors: R. J. Gardner and W. F. Pfeffer
Journal: Trans. Amer. Math. Soc. 259 (1980), 65-74
MSC: Primary 54D20; Secondary 28A35, 54G20
MathSciNet review: 561823
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that in metalindelöf spaces certain questions about Radon measures cannot be decided within the Zermelo-Fraenkel set theory, including the axiom of choice.

References [Enhancements On Off] (What's this?)

  • [AU] P. S. Alexandroff and P. S. Urysohn, Mémoire sur les espaces topologique compacts, Verh. Konink. Nedrl. Akad. Wetensch. Afd. Natuurk. Amsterdam 14 (1929), 1-96.
  • [BL] H. R. Bennet and D. J. Lutzer, A note on weak $ \theta $-refinability, General Topology and Appl. 2 (1972), 49-54. MR 0301697 (46:853)
  • [D] K. J. Devlin, Variations on $ \diamondsuit$, J. Symbolic Logic 44 (1979), 51-58. MR 523488 (80c:03050)
  • [Di] M. A. Dickmann, Large infinitary languages, North-Holland, Amsterdam, 1975. MR 0539973 (58:27450)
  • [G] R. J. Gardner, The regularity of Borel measures and Borel measure-compactness, Proc. London Math. Soc. 30 (1975), 95-113. MR 0367145 (51:3387)
  • [GG] G. Gruenhage and R. J. Gardner, Completeness and weak covering properties, and measure-compactness, J. London Math. Soc. 18 (1978), 316-324. MR 509947 (80d:54021)
  • [GJ] L. Gillman and M. Jerison, Rings of continuous functions, Van Nostrand, Princeton, N. J., 1960. MR 0116199 (22:6994)
  • [GP] G. Gruenhage and W. F. Pfeffer, When inner regularity of Borel measures implies regularity, J. London Math. Soc. 17 (1978), 165-171. MR 485446 (80c:28010)
  • [H] P. R. Halmos, Measure theory, Van Nostrand, Princeton, N. J., 1950. MR 0033869 (11:504d)
  • [Hy] R. Haydon, On compactness in spaces of measures and measure compact spaces, Proc. London Math. Soc. 29 (1974), 1-16. MR 0361745 (50:14190)
  • [J] R. B. Jensen, The fine structure of the constructable universe, Ann. Math. Logic 4 (1972), 229-308. MR 0309729 (46:8834)
  • [K] M. Katětov, Measures in fully normal spaces, Fund. Math. 38 (1951), 73-84. MR 0048531 (14:27c)
  • [Ku] K. Kunen (to appear).
  • [O] A. J. Ostaszewski, On countably compact, perfectly normal spaces, J. London Math. Soc. 14 (1976), 505-516. MR 0438292 (55:11210)
  • [P] W. F. Pfeffer, Integrals and measures, Dekker, New York, 1977. MR 0460580 (57:573)
  • [S] L. Schwartz, Radon measures on arbitrary topological spaces and cylindrical measures, Oxford Univ. Press, London, 1973. MR 0426084 (54:14030)
  • [ST] R. M. Solovay and S. Tennenbaum, Iterated Cohen extensions and Souslin's problem, Ann. of Math. (2) 94 (1971), 201-245. MR 0294139 (45:3212)
  • [T] F. D. Tall, The countable chain condition versus separability-applications of Martin's axiom, General Topology and Appl. 4 (1974), 315-339. MR 0423284 (54:11264)
  • [U] S. Ulam, Zur Masstheorie in der allgemeinen Mengenlehre, Fund. Math. 16 (1930), 140-150.
  • [WW] J. M. Worrel and H. H. Wicke, Characterizations of developable topological spaces, Canad. J. Math. 17 (1965), 820-830. MR 0182945 (32:427)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 54D20, 28A35, 54G20

Retrieve articles in all journals with MSC: 54D20, 28A35, 54G20

Additional Information

Keywords: Borel measure, regular measure, Radon space, metalindelöf space, continuum hypothesis, Martin's axiom, $ \clubsuit$
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society