| Title:
|
What’s the price of a nonmeasurable set? (English) |
| Author:
|
Sardella, Mirko |
| Author:
|
Ziliotti, Guido |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
127 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
41-48 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Lebesgue measure |
| Keyword:
|
nonmeasurable set |
| Keyword:
|
axiom of choice |
| MSC:
|
28A05 |
| MSC:
|
28A20 |
| MSC:
|
28E15 |
| idZBL:
|
Zbl 1006.28003 |
| idMR:
|
MR1895245 |
| DOI:
|
10.21136/MB.2002.133985 |
| . |
| Date available:
|
2009-09-24T21:57:43Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133985 |
| . |
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| . |
