Generic subadditive functions

Abstract

We prove a generalization of the Subadditive Limit Theorem and of the corresponding Berz Theorem in a class of functions that includes both the measurable functions and the Baire functions (those with the Baire property). The generic subadditive functions are defined by a combinatorial property previously introduced for the study of the foundations of regular variation in LSE-CDAM-2006-22. By specialization we thus provide the previously unknown Baire variants of the fundamental theorems of subbaditive functions, answering an old question ([BGT], 2.12.4 p. 123).