I'm reading through the interesting book on statistical mechanics and
computation mentioned earlier on the list:
http://n2.nabble.com/Re%3A--WedTech--A-Winter%27s-Read-td1369555.html
So I found myself brushing up on probability theory, and was amazed to
see what all has gone on since my earlier (like 1960's & 1970's)
reading! The most fascinating point is that measures and sigma
algebras have crept in as a way to better qualify and understand
"events" .. which I always understood to simply be any subset of the
sample space, Omega. Nope. For many probability spaces, not all
subsets qualify as events. Here are some pointers:
http://en.wikipedia.org/wiki/Probability_space
http://en.wikipedia.org/wiki/Sample_space
http://en.wikipedia.org/wiki/Measure_(mathematics)
I particularly like this from the first reference above:
"A probability space is a measure space such that the
measure of the whole space is equal to 1."
Sweet!
This is fascinating .. yet more unification within mathematics. Great
fun to see what all's gone on since grad school. Hopefully this will
help statistic crawl from its grave of the law of large numbers and
the central limit theorem into the light of far more sophisticated,
cleaner mathematics.
-- Owen
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