A NEW NON-MEASURABLE SET AS A VECTOR SPACE

Title & Authors
A NEW NON-MEASURABLE SET AS A VECTOR SPACE
Chung, Soon-Yeong;

Abstract
We use Cauchy's functional equation to construct a new non-measurable set which is a (vector) subspace of $\small{\mathbb{R}}$ and is of a codimensiion 1, considering $\small{\mathbb{R}}$, the set of real numbers, as a vector space over a field $\small{\mathbb{Q}}$ of rational numbers. Moreover, we show that $\small{\mathbb{R}}$ can be partitioned into a countable family of disjoint non-measurable subsets.
Keywords
non-measurable set;
Language
English
Cited by
References
1.
G. de Barra, Measure Theory and Integration, Ellis Horwod Limited, New York, 1981

2.
G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge University Press, New York, 1952