\begin{definition}[Definition:Sequence/Minimizing/Functional/Limit Minimizing Function of]
Let $\sequence {y_n}$ be a minimizing sequence of a functional $J$.
Suppose:
:$\ds \lim_{n \mathop \to \infty} y_n = \hat y$
and
:$\ds \lim_{n \mathop \to \infty} J \sqbrk {y_n} = J \sqbrk {\hat y}$
Then $\hat y$ is the '''limit minimizing function''' of $J \sqbrk {y_n}$ and $J \sqbrk {\hat y} = \mu$.
{{explain|Ambiguous. Does the "and" separate two distinct clauses, or two elements of a list of elements that $\hat y$ is the limit minimizing function of, the second element just happening to equal $\mu$? If the former, then that second clause needs to be separated off into a separate page, and if the latter, make it more obvious that this is a two-element list by presenting it as one.
It is the former. Will see how to reformulate it.}}
\end{definition}