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Results tagged with axiom-of-choice
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user 48485
An important and fundamental axiom in set theory sometimes called Zermelo's axiom of choice. It was formulated by Zermelo in 1904 and states that, given any set of mutually disjoint nonempty sets, there exists at least one set that contains exactly one element in common with each of the nonempty sets. The axiom of choice is related to the first of Hilbert's problems.
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Accepted
Darboux property of non-atomic sigma-additive nonnegative measures equivalent to the AC?
Here is a proof that only uses countable choice. It is taken from Fremlin, Measure Theory, Volume 5, Number 566F. The chapter 56 of this multi-volume work is a great source on the discussion of choice …
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4
votes
Unnecessary uses of the axiom of choice
The supremum of an arbitrary set of measurable functions from a $\sigma$-finite measure space into $\mathbb R\cup \{\pm\infty\}$ exists in the following sense:
Let $F$ be a set of such measurable func …