LECTURE NOTES MEASURE THEORY and PROBABILITY
Definition 2.2. A Lebesgue–Stieltjes measure on R is a measure on B = σ(B 0) such that µ(I) < ∞ for each bounded interval I. By an extended distribution function on R we shall mean a map F:R → R that is increasing, F(a) ≤ F(b) if a<b, and right continuous, lim x→x+ 0 F(x) = F(x 0). If in addition the function F is nonnegative ...
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