  In the direction towards the question when mixed multiplicities are equal to
the Hilbert-Samuel multiplicity of joint reductions, this paper not only
generalizes [28, Theorem 3.1] that covers the Rees's theorem [13, Theorem 2.4],
but also removes the hypothesis that joint reductions are systems of parameters
in [28, Theorem 3.1]. The results of the paper seem to make the problem of
expressing mixed multiplicities into the Hilbert-Samuel multiplicity of joint
reductions become closer.
