  We characterize the atomic probability measure on $\mathbb{R}^d$ which having
a finite number of atoms. We further prove that the Jacobi sequences associated
to the multiple Hermite (resp. Laguerre, resp. Jacobi) orthogonal polynomials
are diagonal matrices. Finally, as a consequence of the multiple Jacobi
orthogonal polynomials case, we give the Jacobi sequences of the
  Gegenbauer, Chebyshev and Legendre orthogonal polynomials.
