Probability
The Analysis of Data, volume 1
Notes
$
\def\P{\mathsf{\sf P}}
\def\E{\mathsf{\sf E}}
\def\Var{\mathsf{\sf Var}}
\def\Cov{\mathsf{\sf Cov}}
\def\std{\mathsf{\sf std}}
\def\Cor{\mathsf{\sf Cor}}
\def\R{\mathbb{R}}
\def\c{\,|\,}
\def\bb{\boldsymbol}
\def\diag{\mathsf{\sf diag}}
\def\defeq{\stackrel{\tiny\text{def}}{=}}
$
E.7. Notes
There are many textbooks that describe rigorously measure theory and its connection to probability theory. A few well known ones are (Feller, 1971), (Breiman, 1992), (Billingsley, 1995), (Ash, 1999), (Resnick, 1999), (Kallenberg, 2002). Our description is closest to (Billingsley, 1995), but is slightly simplified since we focus on probability measures rather than the general case.