Axiom of finite choice

In mathematics, the axiom of finite choice is a weak version of the axiom of choice which asserts that if is a family of non-empty finite sets, then

(set-theoretic product).[1]:14

If every set can be linearly ordered, the axiom of finite choice follows.[1]:17

Applications

An important application is that when is a measure space where is the counting measure and is a function s.t.

,

then for at most countably many .

References

  1. Herrlich, Horst (2006). The axiom of choice. Lecture Notes in Mathematics. 1876. Berlin, Heidelberg: Springer. doi:10.1007/11601562. ISBN 978-3-540-30989-5.
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