概率论 ：基本测度论——测度延拓定理 (5)

Hi everybody, today is the last but one lecture for measure extension theorem. In this lecture, we will recognize another well-known measure which define on Borel σ-algebra on R, the so-called Lebesgue-Stieltjes measure. We will also see that the Lebesgue-Borel measure defined on B(R) is a special case of the Lebesgue-Stieltjes measure. Further, I will give the definitions of proper distribution function and (possibly) defective distribution function, respectively. Finally, we will see that the map from the set of probability measures to the set of distribution functions, respectively from the set of sub-probability measures to the set of defective distribution functions is bijective. Enjoy!