# What’s the price of a nonmeasurable set?

Mirko Sardella; Guido Ziliotti

Mathematica Bohemica (2002)

- Volume: 127, Issue: 1, page 41-48
- ISSN: 0862-7959

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topSardella, Mirko, and Ziliotti, Guido. "What’s the price of a nonmeasurable set?." Mathematica Bohemica 127.1 (2002): 41-48. <http://eudml.org/doc/249032>.

@article{Sardella2002,

abstract = {In this note, we prove that the countable compactness of $\lbrace 0,1\rbrace ^\{\{\mathbb \{R\}\}\}$ together with the Countable Axiom of Choice yields the existence of a nonmeasurable subset of $\{\mathbb \{R\}\}$. This is done by providing a family of nonmeasurable subsets of $\{\mathbb \{R\}\}$ whose intersection with every non-negligible Lebesgue measurable set is still not Lebesgue measurable. We develop this note in three sections: the first presents the main result, the second recalls known results concerning non-Lebesgue measurability and its relations with the Axiom of Choice, the third is devoted to the proofs.},

author = {Sardella, Mirko, Ziliotti, Guido},

journal = {Mathematica Bohemica},

keywords = {Lebesgue measure; nonmeasurable set; axiom of choice; Lebesgue measure; nonmeasurable set; axiom of choice},

language = {eng},

number = {1},

pages = {41-48},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {What’s the price of a nonmeasurable set?},

url = {http://eudml.org/doc/249032},

volume = {127},

year = {2002},

}

TY - JOUR

AU - Sardella, Mirko

AU - Ziliotti, Guido

TI - What’s the price of a nonmeasurable set?

JO - Mathematica Bohemica

PY - 2002

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 127

IS - 1

SP - 41

EP - 48

AB - In this note, we prove that the countable compactness of $\lbrace 0,1\rbrace ^{{\mathbb {R}}}$ together with the Countable Axiom of Choice yields the existence of a nonmeasurable subset of ${\mathbb {R}}$. This is done by providing a family of nonmeasurable subsets of ${\mathbb {R}}$ whose intersection with every non-negligible Lebesgue measurable set is still not Lebesgue measurable. We develop this note in three sections: the first presents the main result, the second recalls known results concerning non-Lebesgue measurability and its relations with the Axiom of Choice, the third is devoted to the proofs.

LA - eng

KW - Lebesgue measure; nonmeasurable set; axiom of choice; Lebesgue measure; nonmeasurable set; axiom of choice

UR - http://eudml.org/doc/249032

ER -

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