Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Products of completion regular measures


Author: Constantinos Gryllakis
Journal: Proc. Amer. Math. Soc. 103 (1988), 563-568
MSC: Primary 28C15; Secondary 28A35
DOI: https://doi.org/10.1090/S0002-9939-1988-0943085-0
MathSciNet review: 943085
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ X = {\prod _{i \in I}}{X_i}$ and $ Y = {\prod _{j \in J}}{Y_j}$, where all $ {X_i},{Y_j}$ are separable metric spaces. Let $ \mu $ and $ \nu $ be completion regular Radon probability measures on $ X$ and $ Y$ respectively. Then $ \mu \times \nu $ on $ X \times Y$ is completion regular.

This solves a problem of J. R. Choksi and D. H. Fremlin.


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

  • [1] J. R. Choksi, Problem 1 in "Problem Section", Measure theory and its applications (J. M. Belley, J. Dubois and P. Morales, eds.), Lecture Notes in Math., vol. 1033, Springer-Verlag, Berlin and New York. MR 729520 (84k:28001)
  • [2] -, Recent developments arising out of Kakutani work on completion regularity of measure, Contemp. Math., vol. 26, Amer. Math. Soc., Providence, R.I., 1984, pp. 81-94.
  • [3] J. R. Choksi and D. H. Fremlin, Completion regular measures on product spaces, Math. Ann. 241 (1979), 113-128. MR 534807 (81m:28004)
  • [4] W. W. Comfort and S. Negrepontis, The theory of ultrafilters, Springer-Verlag, Berlin and New York, 1984. MR 0396267 (53:135)
  • [5] P. Erdös and J. C. Oxtoby, Partitions of the plane into sets having positive measure in every non-null measurable product set, Trans. Amer. Math. Soc. 79 (1955), 91-102. MR 0072928 (17:352f)
  • [6] D. H. Fremlin, Products of Radon measures: a counter-example, Canad. Math. Bull 19 (1976), 285-289. MR 0435332 (55:8292)
  • [7] S. Kakutani, Notes on infinite product measures. II, Proc. Imperial Acad. Tokyo 19 (1943), 184-188. MR 0014404 (7:279g)
  • [8] K. A. Ross and A. H. Stone, Products of separable spaces, Amer. Math. Monthly 71 (1964), 398-403. MR 0164314 (29:1611)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28C15, 28A35

Retrieve articles in all journals with MSC: 28C15, 28A35


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0943085-0
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society