Well, sure.  But the point is that the axiom of choice asserts, merely, the 
existence of the ability to choose a subset.  They call them "choice 
functions", as if there exists some "chooser".  But there's no sense of time 
(before the choice function is applied versus after it's applied).  The name 
"choice" is a misleading misnomer.

And that's my point.  Probability theory is a special case of measure theory.  
Calling the set measures "probabilities" is an antiquated, misleading, and 
unfortunate name.

On 12/14/2016 01:41 PM, Frank Wimberly wrote:
> Don't think about choosing.  The axiom of choice says that there is a 
> function from each set (subset) to an element of itself, as I recall.

-- 
☣ glen

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