| Title:
|
When is $\Bbb R$ the union of an increasing family of null sets? (English) |
| Author:
|
González-Hernández, Juan |
| Author:
|
Hernández-Hernández, Fernando |
| Author:
|
Villarreal, César E. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
48 |
| Issue:
|
4 |
| Year:
|
2007 |
| Pages:
|
623-630 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Sierp'nski set |
| Keyword:
|
null sets |
| Keyword:
|
random forcing |
| Keyword:
|
rational perfect set forcing |
| Keyword:
|
Miller forcing |
| MSC:
|
03E35 |
| MSC:
|
28A05 |
| idZBL:
|
Zbl 1199.28003 |
| idMR:
|
MR2375163 |
| . |
| Date available:
|
2009-05-05T17:05:10Z |
| Last updated:
|
2012-05-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119685 |
| . |
| Reference:
|
[BJ95] Bartoszyński T., Judah H.: Set Theory: On the Structure of the Real Line.A K Peters Ltd., Wellesley, MA, 1995. MR 1350295 |
| Reference:
|
[Hru07] Hrušák M.: Personal communication.2007. |
| Reference:
|
[JS94] Judah H., Shelah S.: Killing Luzin and Sierpiński sets.Proc. Amer. Math. Soc. 120 (1994), 3 917-920. Zbl 0797.03050, MR 1164145 |
| Reference:
|
[Kun83] 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. Zbl 0534.03026, MR 0597342 |
| Reference:
|
[Oxt80] 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. Zbl 0435.28011, MR 0584443 |
| Reference:
|
[Piu97] 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. Zbl 0894.93001, MR 1472738 |
| Reference:
|
[Roy88] Royden H.L.: Real Analysis.third ed., Macmillan Publishing Company, New York, 1988. MR 1013117 |
| . |
