  The problem of recovering a moment-determinate multivariate function $f$ via
its moment sequence is studied. Under mild conditions on $f$, the point-wise
and $L_1$-rates of convergence for the proposed constructions are established.
The cases where $f$ is the indicator function of a set, and represents a
discrete probability mass function are also investigated. Calculations of the
approximants and simulation studies are conducted to graphically illustrate the
behavior of the approximations in several simple examples. Analytical and
simulated errors of proposed approximations are recorded in Tables 1-3.
