Powers of transitive bases of measure and category

Pawlikowski, Janusz

doi:10.1090/S0002-9939-1985-0776210-2

Powers of transitive bases of measure and category
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by Janusz Pawlikowski PDF

Proc. Amer. Math. Soc. 93 (1985), 719-729 Request permission

Abstract:

We prove that on the real line the minimal cardinality of a base of measure zero sets equals the minimal cardinality of their transitive base. Next we show that it is relatively consistent that the minimal cardinality of a base of meager sets is greater than the minimal cardinality of their transitive base. We also prove that it is relatively consistent that the transitive additivity of measure zero sets is greater than the ordinary additivity and that the same is true about meager sets.

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