Document Type

Article

Publication Date

1982

Keywords

Lebesgue nonmeasurable subsets, Vitali's proof

Abstract

Many proofs of the fact that there exist Lebesgue nonmeasurable subsets of the real line are known. The oldest proof of this result is due to Vitali [4]. The cosets (under addition) of Q, the set of rational numbers, constitute a partition of the line into an uncountable family of disjoint sets, each congruent to Q under translation, Vitali's proof shows that V is nonmeasurable, if V is a set having one and only one element in common with each of these cosets.

Publication Title

Radovi

Volume

Nauka LXIX

First Page

39

Last Page

43

Required Publisher's Statement

Published by: Academy of Arts and Sciences of Bosnia and Herzegovina and Department of Mathematics, University of Sarajevo, Sarajevo, Bosnia and Herzegovina (Akad. Nauka Umjet. Bosne Hercegov. Rad. Odjelj. Prirod. Mat. Nauka LXIX (1982) 39-43)

Subjects - Topical (LCSH)

Measure theory; Transfinite numbers

Genre/Form

articles

Type

Text

Rights

Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.

Language

English

Format

application/pdf

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Mathematics Commons

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