Axiom of finite choice
In mathematics, the axiom of finite choice is a weak version of the axiom of choice which asserts that if formula_1 is a family of non-empty "finite sets", then If every set can be linearly ordered, the axiom of finite choice follows. Applications. An important application is that when formula_3 is a measure space where formula_4 is the counting measure and formula_5 is a function such that then formula_7 for at most countably many formula_8.