Let
G
G
be a compact abelian group, and
Γ
\Gamma
its character group. Given
E
⊂
Γ
,
E
a
E \subset \Gamma ,{E^a}
denotes the set of all accumulation points of
E
E
in
Γ
¯
\overline \Gamma
, the Bohr compactification of
Γ
\Gamma
. In this paper it is shown that the inclusion
(
L
1
(
G
)
)
∧
|
E
⊂
(
l
1
(
G
)
)
∧
|
E
{({L^1}(G))^ \wedge }{|_E} \subset {({l^1}(G))^ \wedge }{|_E}
obtains if and only if
E
∩
E
a
=
∅
E \cap {E^a} = \emptyset
and there exists a measure
μ
ϵ
M
(
G
)
\mu \epsilon M(G)
such that
μ
^
=
1
\widehat \mu = 1
on
E
E
and
μ
^
=
0
\widehat \mu = 0
on
Γ
∩
E
a
\Gamma \cap {E^a}
.