<s>
In	O
mathematical	O
analysis	O
,	O
epi-convergence	B-Algorithm
is	O
a	O
type	O
of	O
convergence	O
for	O
real-valued	O
and	O
extended	O
real-valued	O
functions	O
.	O
</s>
<s>
Epi-convergence	B-Algorithm
is	O
important	O
because	O
it	O
is	O
the	O
appropriate	O
notion	O
of	O
convergence	O
with	O
which	O
to	O
approximate	O
minimization	O
problems	O
in	O
the	O
field	O
of	O
mathematical	O
optimization	O
.	O
</s>
<s>
Mosco	O
convergence	O
is	O
a	O
generalization	O
of	O
epi-convergence	B-Algorithm
to	O
infinite	O
dimensional	O
spaces	O
.	O
</s>
<s>
The	O
following	O
extension	O
allows	O
epi-convergence	B-Algorithm
to	O
be	O
applied	O
to	O
a	O
sequence	O
of	O
functions	O
with	O
non-constant	O
domain	O
.	O
</s>
<s>
In	O
fact	O
,	O
epi-convergence	B-Algorithm
coincides	O
with	O
the	O
-convergence	O
in	O
first	O
countable	O
spaces	O
.	O
</s>
<s>
Epi-convergence	B-Algorithm
is	O
the	O
appropriate	O
topology	O
with	O
which	O
to	O
approximate	O
minimization	O
problems	O
.	O
</s>
<s>
Epi-convergence	B-Algorithm
provides	O
an	O
answer	O
to	O
the	O
question	O
:	O
In	O
what	O
sense	O
should	O
the	O
approximations	O
converge	O
to	O
the	O
original	O
problem	O
in	O
order	O
to	O
guarantee	O
that	O
approximate	O
solutions	O
converge	O
to	O
a	O
solution	O
of	O
the	O
original	O
?	O
</s>
<s>
Epi-convergence	B-Algorithm
is	O
the	O
weakest	O
notion	O
of	O
convergence	O
for	O
which	O
this	O
result	O
holds	O
.	O
</s>
<s>
In	O
general	O
,	O
epi-convergence	B-Algorithm
neither	O
implies	O
nor	O
is	O
implied	O
by	O
pointwise	B-Algorithm
convergence	I-Algorithm
.	O
</s>
<s>
Additional	O
assumptions	O
can	O
be	O
placed	O
on	O
an	O
pointwise	O
convergent	O
family	O
of	O
functions	O
to	O
guarantee	O
epi-convergence	B-Algorithm
.	O
</s>
