Pathology of submeasures and Fσ ideals

We address some phenomena about the interaction between lower semicontinuous submeasures on N N and Fσ F σ ideals. We analyze the pathology degree of a submeasure and present a method to construct pathological Fσ F σ ideals. We give a partial answers to the question of whether every nonpathological tall Fσ F σ ideal is Katětov above the random ideal or at least has a Borel selector. Finally, we show a representation of nonpathological Fσ F σ ideals using sequences in Banach spaces.