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