Definition:Sequence/Minimizing/Functional/Limit Minimizing Function of

Definition
Let $ \left \{ { y_n } \right \} $ be a minimizing sequence of a functional $ J $.

Suppose:


 * $ \displaystyle \lim_{ n \to \infty } y_n = \hat{ y }$.

and


 * $ \displaystyle \lim_{ n \to \infty } J \left [ { y_n } \right ] = J \left [ { \hat { y } } \right ] $

Then $ \hat{ y } $ is the limit minimizing function of $ J \left [ { y_n } \right ] $ and $ J \left[ { \hat { y } } \right ] = \mu $.