- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnline Submission ㆍMy Manuscript - For Reviewers - For Editors
 A new non-measurable set as a vector space Commun. Korean Math. Soc. 2006 Vol. 21, No. 3, 429-432 Printed September 1, 2006 Soon-Yeong Chung Sogang University Abstract : We use Cauchy's functional equation to construct a new non-measurable set which is a (vector) subspace of $\Bbb R$ and is of a codimension 1, considering $\Bbb R$, the set of real numbers, as a vector space over a field $\Bbb Q$ of rational numbers. Moreover, we show that ${\Bbb R}$ can be partitioned into a countable family of disjoint non-measurable subsets. Keywords : non-measurable set MSC numbers : 28A05 Downloads: Full-text PDF

 Copyright © Korean Mathematical Society. The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd