2014/05/12 by Jabłońska, Eliza
#28C10 #28E05 #54B30 #54E52 #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN)
paper · doi:10.48550/arxiv.1405.2939
In the paper we would like to pay attention to some analogies between Haar meager sets and Haar null sets. Among others, we will show that 0∈ \inn (A-A) for each Borel set A, which is not Haar meager in an abelian Polish group. Moreover, we will give an example of a Borel non-Haar meager set A⊂ c0 such that \inn (A+A)=∅. Finally, we will define D-measurability as a topological analog of Christensen measurability, and apply our generalization of Piccard's theorem to prove that each D-measurable homomorphism is continuous. Our results refer to the papers \citeCh, \citeDarji and \citeFS.