Coneability of Anti-Fubini Functions and Other Lineability Properties

Abstract

It is proved that the family of measurable real functions on the product measure space satisfying (or not) the conclusion of Fubini’s Theorem (along with a number of related families) is algebraically large, in the sense that it contains large convex cones or even large vector subspaces (except for zero) under rather general assumptions. Several earlier related results are improved, mainly regarding the cardinality of the generator set of the corresponding cones or subspaces.