Abstract
Distribution functions are mathematical artifacts with properties that are independent of any probabilistic setting. Notwithstanding, most of the theorems of interest are geared to d.f.s of r.v.s and the majority of proofs are simpler and more intuitive when couched in terms of r.v.s having, or probability measures determined by, the given d.f.s. Since r.v.s possessing preassigned d.f.s can always be defined on some probability space, the language of r.v.s and probability will be utilized in many of the proofs without further ado.
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Chow, Y.S., Teicher, H. (1997). Distribution Functions and Characteristic Functions. In: Probability Theory. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1950-7_8
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