The theorem of the approximation of Müntz-Szász is a basic result of the Théorie of the approximation which was discovered by Hermann Müntz in 1914 then by Otto Szász in 1916. This theorem had been conjectured in this form by Sergeï Natanovitch Bernstein.

Either $I$ a segment of $\backslash \; mathbb\; \{R\}$, the Théorème of Weierstrass ensures that any function continues $I$ in $\backslash \; mathbb\; \{C\}$ is limiting uniform of a succession of polynomials.

Theorem of Mûntz ensures that, more generally, if a succession of distinct realities $\backslash \; lambda\_n$ is such as the series $\backslash \; sum\; \backslash \; frac\; \{1\}\; \{\backslash \; lambda\; \_n\}$ diverges, then any continuous function on $I$ is limiting uniform of a succession of linear combinations of the functions $f\_n\; (X)\; =x^\; \{\backslash \; lambda\_n\}$.