#### Document Type

Article

#### Publication Date

1982

#### 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)**

#### Recommended Citation

Ćurgus, Branko and Miller, Harry I., "Nonmeasurable Sets and Pairs of Transfinite Sequences" (1982). *Mathematics.* Paper 78.

http://cedar.wwu.edu/math_facpubs/78