  We introduce the twisted Bernoulli measures as a family of p-adic measures
parametrized by the complement of the open disc with radius 1 and centered at 1
in the completion of an algebraic closure of p-adic numbers. These measures are
the higher order versions of the measure used by Koblitz and Coleman to
interpret (p-adic) polylogarithms. We also prove that these measures are the
unique p-adic measures that can be obtained from polynomials over the field
Q(y) which is similar to the uniqueness property of Bernoulli measures.
