Levin, Przytycki and Shen [Invent. Math. 205 (2016), pp. 363–382] proved for a polynomial map
f
c
(
z
)
=
z
d
+
c
f_c(z)=z^d+c
,
d
≥
2
d\geq 2
and
c
∈
C
c \in \mathbb C
, with Julia set
J
(
f
)
J(f)
of positive measure that for a.e.
z
∈
J
(
f
)
z \in J(f)
the Lyapunov exponent
χ
s
(
z
)
=
0
\chi _s(z)=0
. The aim of this paper is to show that the extension to non-entire transcendental meromorphic functions is not possible.