[FOM] Brouwer's choice sequences as a basis for measure theory and probability theory

[Giovanni Lagnese]

In considering problems regarding the foundations of probability, I have 
thought that Brouwer's choice sequences could be an interesting basis 
for measure theory and probability theory. The class of choice sequences 
can be regarded both as the codomain and (in essence) as the domain of 
probability functions. A such approach could suggest possible solutions 
to some classical (and nonstandard) measure and probability foundational 
problems, such as that of the mostly forcedly "dogmatic" (or 
"definitively" infinitesimal) prior assignments in a probability space. 
Why don't develop a measure theory and a probability theory based on 
choice sequences? Why not?

Giovanni Lagnese 


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