When is the union of an increasing family of null sets?
Juan González-Hernández; Fernando Hernández-Hernández; César E. Villarreal
Commentationes Mathematicae Universitatis Carolinae (2007)
- Volume: 48, Issue: 4, page 623-630
- ISSN: 0010-2628
Access Full Article
top
Abstract
topHow to cite
topGonzález-Hernández, Juan, Hernández-Hernández, Fernando, and Villarreal, César E.. "When is $\mathbb {R}$ the union of an increasing family of null sets?." Commentationes Mathematicae Universitatis Carolinae 48.4 (2007): 623-630. <http://eudml.org/doc/250209>.
@article{González2007,
abstract = {We study the problem in the title and show that it is equivalent to the fact that every set of reals is an increasing union of measurable sets. We also show the relationship of it with Sierpi'nski sets.},
author = {González-Hernández, Juan, Hernández-Hernández, Fernando, Villarreal, César E.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Sierp'nski set; null sets; random forcing; rational perfect set forcing; Miller forcing; Sierpiński set; null sets; random forcing; rational perfect set forcing; Miller forcing},
language = {eng},
number = {4},
pages = {623-630},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {When is $\mathbb \{R\}$ the union of an increasing family of null sets?},
url = {http://eudml.org/doc/250209},
volume = {48},
year = {2007},
}
TY - JOUR
AU - González-Hernández, Juan
AU - Hernández-Hernández, Fernando
AU - Villarreal, César E.
TI - When is $\mathbb {R}$ the union of an increasing family of null sets?
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2007
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 48
IS - 4
SP - 623
EP - 630
AB - We study the problem in the title and show that it is equivalent to the fact that every set of reals is an increasing union of measurable sets. We also show the relationship of it with Sierpi'nski sets.
LA - eng
KW - Sierp'nski set; null sets; random forcing; rational perfect set forcing; Miller forcing; Sierpiński set; null sets; random forcing; rational perfect set forcing; Miller forcing
UR - http://eudml.org/doc/250209
ER -
References
top- Bartoszyński T., Judah H., Set Theory: On the Structure of the Real Line, A K Peters Ltd., Wellesley, MA, 1995. MR1350295
- Hrušák M., Personal communication, 2007.
- Judah H., Shelah S., Killing Luzin and Sierpiński sets, Proc. Amer. Math. Soc. 120 (1994), 3 917-920. (1994) Zbl0797.03050MR1164145
- Kunen K., Set Theory: An Introduction to Independence Proofs, Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland Publishing Co., Amsterdam, 1983, reprint of the 1980 original. Zbl0534.03026MR0597342
- Oxtoby J.C., Measure and Category. A Survey of the Analogies between Topological and Measure Spaces, second ed., Graduate Texts in Mathematics, vol. 2, Springer, New York-Berlin, 1980. Zbl0435.28011MR0584443
- Piunovskiy A.B., Optimal Control of Random Sequences in Problems with Constraints, Mathematics and its Applications, vol. 410, Kluwer Academic Publishers, Dordrecht, 1997, with a preface by V.B. Kolmanovskii and A.N. Shiryaev. Zbl0894.93001MR1472738
- Royden H.L., Real Analysis, third ed., Macmillan Publishing Company, New York, 1988. MR1013117
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.