Theoretical Statistics pp 1-24 | Cite as

# Probability and Measure

## Abstract

Much of the theory of statistical inference can be appreciated without a detailed understanding of probability or measure theory. This book does not treat these topics with rigor. But some basic knowledge of them is quite useful. Much of the literature in statistics uses measure theory and is inaccessible to anyone unfamiliar with the basic notation. Also, the notation of measure theory allows one to merge results for discrete and continuous random variables. In addition, the notation can handle interesting and important applications involving censoring or truncation in which a random variable of interest is neither discrete nor continuous. Finally, the language of measure theory is necessary for stating many results correctly. In the sequel, measure-theoretic details are generally downplayed or ignored in proofs, but the presentation is detailed enough that anyone with a good background in probability should be able to fill in any missing details.

## Keywords

Probability Measure Lebesgue Measure Cumulative Distribution Function Random Vector Mass Function## Preview

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