#### Ray Vickson

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I think that Cox/Jaynes is "equivalent" to probability as done in volume I of Feller---and that is saying a lot. However, some "deeper" modern results (seem to) need the "measure-theoretic" apparatus, so would essentially be rejected by Jaynes. Certainly, the two approaches would no longer be equivalent in any easily-described sense.Yay! Gotta love Cox & Jaynes!! Hooray to them! I somehow suspect that Kolmogorov and Cox/Jaynes are equivalent, as (I suspect) they come to the same conclusions through (I suspect) different axiomatic processes, but I did find Cox infinitely easier to grasp.

Admittedly, some treatments in the modern way of doing things look like they might just be re-statements of results done in the old-fashioned way, but the resulting statements of the results are more cumbersome in the old way. For example, Feller, Vol. I, proves the so-called Strong Law of Large Numbers without using any measure theory or other more abstract methods. However, the result looks less appealing than the modern statement. The modern statement would amount to ##P(\lim_{n \to \infty} \bar{X}_n = \mu) = 1.## In pre-measure language the same result would say "For every ##\epsilon > 0## with probability 1 there occur only finitely many of the events ##|\bar{X}_n - \mu| > \epsilon##" How much nicer is the first way of saying it compared with the second way.