Relationship between measurable sets in the Lebesgue sense and sets with the Baire property on the real line

Abstract

This thesis is based on some concepts from real analysis and topology on the real line R. The goal is to clarify the relationship between the family L(R) of Lebesgue measurable sets and the family Bp(R) of sets possessing the Baire property there. In the text we observe some common properties of these families as well as common properties of their complements in the power set P(R) of all subsets of the real line. The thesis ends by a theorem which shows that despite of all similarities the family L(R) of Lebesgue measurable sets and the family Bp(R) of sets possessing the Baire property are completely di erent.