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Brouwer's choice sequences as a basis for measure theory and probability theory
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Giovanni Lagnese
Aug 23, 2010, 9:30:05 AM8/23/10
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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?
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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