Measure Zero Sets Whose Algebraic Sum Is Non-Measurable

Authors

Krzysztof Ciesielski, West Virginia UniversityFollow

Document Type

Article

Publication Date

2001

College/Unit

Eberly College of Arts and Sciences

Department/Program/Center

Mathematics

Abstract

In this note we will show that for every natural number n > 0 there exists an S ⊂ [0, 1] such that its n-th algebraic sum nS = S + ··· + S is a nowhere dense measure zero set,but its n+ 1-st algebraic sum nS +S is neither measurable nor it has the Baire property. In addition,the set S will be also a Hamel base,that is,a linear base of R over Q.

Digital Commons Citation

Ciesielski, Krzysztof, "Measure Zero Sets Whose Algebraic Sum Is Non-Measurable" (2001). Faculty & Staff Scholarship. 837.
https://researchrepository.wvu.edu/faculty_publications/837