A NEW NON-MEASURABLE SET AS A VECTOR SPACE
A NEW NON-MEASURABLE SET AS A VECTOR SPACE
We use Cauchy's functional equation to construct a new non-measurable set which is a (vector) subspace of <TEX>\mathbb{R}$</TEX> and is of a codimensiion 1, considering <TEX>\mathbb{R}$</TEX>, the set of real numbers, as a vector space over a field <TEX>\mathbb{Q}$</TEX> of rational numbers. Moreover, we show that <TEX>\mathbb{R}$</TEX> can be partitioned …