For ideals on omega, meagerness is equivalent to the Misik-Toth condition and to the comeagerness of the set of maldistributed sequences.
Borodulin-Nadzieja, B
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On maldistributed sequences and meager ideals
For ideals on omega, meagerness is equivalent to the Misik-Toth condition and to the comeagerness of the set of maldistributed sequences.