The Müntz–Szász theorem is a basic result of approximation theory, proved by Herman Müntz in 1914 and Otto Szász (1884–1952) in 1916.
The form of the result had been conjectured by Sergei Bernstein before it was proved.
The theorem, in a special case, states that a necessary and sufficient condition for the monomials to span a dense subset of the Banach space C[a,b] of all continuous functions with complex number values on the closed interval [a,b] with a > 0, with the uniform norm, is that the sum of the reciprocals, taken over S, should diverge, i.e. S is a large set.
More generally, one can take exponents from any strictly increasing sequence of positive real numbers, and the same result holds.
Szász showed that for complex number exponents, the same condition applied to the sequence of real parts.