Covering Baire 1 functions with Darboux functions and the cofinality of the ideal of meager sets


Francis Jordan

J. Appl. Anal. 5(1) (1999), 71-94.

Let Dar stand for the Darboux Baire class 1 functions. We show that the cofinality of the meager sets in R is the smallest cardinality of a set of Baire class 1 functions F such that for any finite collection of Baire class 1 functions Gthere is an f in F such that G is a subset of f+Dar. Other results of this type are shown. These results are then considered as statements about additivity. The notion of super-additivity is introduced.

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