Pathology of submeasures and Fσ ideals.

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