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Probability is a measure defined on sample space Sample Space S Event E ⊂ S Probability Function P: P(Φ) = 0 P(S) = 1 E ⊂ F → P(E) ≤ P(F) E ∩ F = Φ → P(E ∪ F) = P(E) + P(F) impossible event sure event monotoneity additivity Universal Set [0, 1] Drop a unit of mass on [0, 1] Subset E ⊂ [0, 1] Mass Function m: m(Φ) = 0 m([0, 1]) = 1 E ⊂ F → m(E) ≤ m(F) E ∩ F = Φ → m(E ∪ F) = m(E) + m(F)
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