Given a
\sigma
σ
-finite measure space
(\Omega, \mathcal{T}, \mu)
(
Ω
,
T
,
μ
)
endowed with a
\mu
μ
-complete tribe, a separable Banach space
E
E
, we consider a topological vector space
(X,T)
(
X
,
T
)
,
X
X
being a decomposable subspace of measurable
E
E
-valued functions defined on
\Omega
Ω
. Under a reasonable assumption on the vector topology
T
T
, we show that if
{(f_{n})}_{n}
(
f
n
)
n
is a sequence of extended real-valued measurable integrands defined on the product
\Omega\times E
Ω
×
E
, with upper epi-limit (or upper
\Gamma
Γ
-limit)
f=ls_{e} f_{n}
f
=
l
s
e
f
n
, then
I_f
I
f
is in many cases an upper bound for the
T
T
-upper epi-limit of the sequence
(I_{f_{n}})_n
(
I
f
n
)
n
, where
I_f
I
f
,
I_{f_{n}}
I
f
n
are the integral functionals defined on
X
X
associated to the integrands
f
f
,
f_n
f
n
. The cases of Lebesgue spaces endowed with its strong, weak, or Mackey topologies are reached. We discuss also the necessity of the given conditions.