Müntz's Theorem

Müntz's theorem is a generalization of the Weierstrass approximation theorem, which states that any continuous function on a closed and bounded interval can be uniformly approximated by polynomials involving constants and any infinite sequence of powers whose reciprocals diverge.

In technical language, Müntz's theorem states that the Müntz space  is dense in  iff

REFERENCES:

Borwein, P. and Erdélyi, T. "Müntz's Theorem." §4.2 in Polynomials and Polynomial Inequalities. New York: Springer-Verlag, pp. 171-205, 1995.