Axioms of probability theory

• Kolmogorov, 1933

  • P(a) >= 0 where a is an event
  • P(l) = 1 where l is the certain event
  • P(a + b) = P(a) + P(b) where a and b are mutually exclusive

• Kolmogorov (axiomatic) definition is computable

  • Probability theory forms the basis for information theory
  • Classical definition (Bernoulli) is uncomputable:

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