\begin{definition}[Definition:Almost Everywhere]
Let $\struct {X, \Sigma, \mu}$ be a measure space.
A property $\map P x$ of elements of $X$ is said to hold '''($\mu$-)almost everywhere''' if the set:
:$\set {x \in X: \neg \map P x}$
of elements of $X$ such that $P$ does not hold is contained in a $\mu$-null set.
\end{definition}