Let
M
(
X
,
G
)
M(X,G)
be the set of
G
G
-invariant means on
L
∞
(
X
,
B
,
P
)
{L^\infty }(X,\mathcal {B},P)
, where
G
G
is a countable group acting ergodically as measure preserving transformations on a nonatomic probability space
(
X
,
B
,
P
)
(X,\mathcal {B},P)
. We show that if there exists
μ
∈
M
(
X
,
G
)
,
μ
≠
P
\mu \in M(X,G),\mu \ne P
, then
M
(
X
,
G
)
M(X,G)
contains an isometric copy of
β
N
∖
N
\beta N\backslash N
, where
β
N
∖
N
\beta N\backslash N
is considered as a subset of
(
l
∞
)
∗
{({l^\infty })^*}
. This provides an answer to a question raised by J. Rosenblatt in 1981.