Proceedings of the American Mathematical Society

Author(s): Piotr Zakrzewski
Journal: Proc. Amer. Math. Soc. 129 (2001), 271-278.
MSC (2000): Primary 03E35, 54E52; Secondary 28A05
Posted: June 14, 2000
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Abstract: We prove that if ZFC is consistent so is ZFC + ``for any sequence $(A_{n})$ of subsets of a Polish space $\langle X,\tau\rangle$ there exists a separable metrizable topology $\tau'$ on

with $\mathbf{B}(X,\tau)\subseteq\mathbf{B}(X,\tau')$ , $\operatorname{MGR}(X,\tau')\cap\mathbf{B}(X,\tau)=\operatorname{MGR} (X,\tau)\cap\mathbf{B}(X,\tau)$ and $A_{n}$ Borel in $\tau'$ for all

.'' This is a category analogue of a theorem of Carlson on the possibility of extending Lebesgue measure to any countable collection of sets. A uniform argument is presented, which gives a new proof of the latter as well.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 03E35, 54E52, 28A05

Piotr Zakrzewski
Affiliation: Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland
Email: piotrzak@mimuw.edu.pl

DOI: 10.1090/S0002-9939-00-05505-2
PII: S 0002-9939(00)05505-2
Keywords: Measure and category, Borel sets, Baire Property, $\sigma$-algebra, $\sigma$-ideal
Received by editor(s): July 10, 1998
Received by editor(s) in revised form: March 16, 1999
Posted: June 14, 2000
Additional Notes: The author was partially supported by KBN grant 2 P03A 047 09 and by the Alexander von Humboldt Foundation
Communicated by: Carl G. Jockusch, Jr.
Copyright of article: Copyright 2000, American Mathematical Society

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