# When is $\mathbb{R}$ 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

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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

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- 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

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