The Miintz-Szasz problem

A remarkable extension of the Weierstrass theorem is the theorem of Miintz [67], according to which the system of the powers

where 0 < < //2 < - - -, is dense in Co[0, 1] = ( / E G'fO, 1]: /(0 ) = 0) if and only if

00 I V — = oo.