We study frequent hypercyclicity in the context of strongly continuous
semigroups of operators. More precisely, we give a criterion (sufficient
condition) for a semigroup to be frequently hypercyclic, whose formulation
depends on the Pettis integral. This criterion can be verified in certain cases
in terms of the infinitesimal generator of semigroup. Applications are given
for semigroups generated by Ornstein-Uhlenbeck operators, and especially for
translation semigroups on weighted spaces of p-integrable functions, or
continuous functions that, multiplied by the weight, vanish at infinity
