PHL246H1 Lecture 8: lec8.pdf
Document Summary
Alexandrey kolmogorov (1903-1987) provides the rst axiomatization of the probability calculus. Alexandrey kolmogorov (1903-1987) provides the rst axiomatization of the probability calculus. (cid:73) probabilities can be de ned on the semantic framework of an algebra of propositions as well as on the syntactic framework of a formal language. A, b, ai w , i n: Kolmogorov (cid:73) in his grundbegriffe der wahrscheinlichkeitsrechnung (1933) (foundations of the theory of probability) A, b, ai w , i n: (cid:73) 1. A = w \ a a, if a a, 3. A, b, ai a, i n: The probability calculus (cid:73) a function pr : a r on a(n) ( -) algebra a of propositions over w into the real numbers r is a ( -additive) probability measure on a iff for all. A, b, ai a, i n: (cid:73) 1. Pr (w ) = 1 (normalization) (cid:73) 3.
