Page "Axiom of choice" Paragraph 76

There are several weaker statements that are not equivalent to the axiom of choice, but are closely related.

One example is the axiom of dependent choice ( DC ).

A still weaker example is the axiom of countable choice ( AC < sub > ω </ sub > or CC ), which states that a choice function exists for any countable set of nonempty sets.

These axioms are sufficient for many proofs in elementary mathematical analysis, and are consistent with some principles, such as the Lebesgue measurability of all sets of reals, that are disprovable from the full axiom of choice.