Appendix A

# Results From Analysis and Probability

## A.1 Some Important Results in Integration Theory

Theorem A.1.1

Lebesgue Dominated Convergence

Let { fn}be a sequence of integrable functions on $\mathcal{X}$. If

(i) ${lim}_{n\to \infty }{f}_{n}\left(x\right)=f\left(x\right)$ a.e. in $\mathcal{X}$, that is, for all $x\notin \mathcal{S}$ where ${\int }_{S}dx=0$, and

(ii) there is an integrable function g on $\mathcal{X}$ such that | fn(x)|≤ g(x) for all ...

Get Theory and Methods of Statistics now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.