  For the integrable higher-spin XXX and XXZ spin chains we present
multiple-integral representations for the correlation function of an arbitrary
product of Hermitian elementary matrices in the massless ground state. We give
a formula expressing it by a single term of multiple integrals. In particular,
we explicitly derive the emptiness formation probability (EFP). We assume
$2s$-strings for the ground-state solution of the Bethe ansatz equations for
the spin-$s$ XXZ chain, and solve the integral equations for the spin-$s$
Gaudin matrix.
  In terms of the XXZ coupling $\Delta$ we define $\zeta$ by $\Delta=\cos
\zeta$, and put it in a region $0 \le \zeta < \pi/2s$ of the gapless regime:
$-1 < \Delta \le 1$ ($0 \le \zeta < \pi$), where $\Delta=1$ ($\zeta=0$)
corresponds to the antiferromagnetic point. We calculate the zero-temperature
correlation functions by the algebraic Bethe ansatz, introducing the Hermitian
elementary matrices in the massless regime, and taking advantage of the fusion
construction of the $R$-matrix of the higher-spin representations of the affine
quantum group.
