If is a weight function (id est a non-negative integrable function) on , then the doubling property means that for some constant ,
for all intervals , where denotes the “doubled” interval (twice enlarged from its center). The constant is referred to as the doubling constant of . It is shown that for those doubling weights, the zeros of the associated orthogonal polynomials are uniformly spaced, which means that if with are the zeros of the -th orthogonal polynomial associated with , then . It is also shown that for doubling weights, neighbouring Cotes numbers are of the same order. In fact, it is shown that these two properties are actually equivalent to the doubling property of the weight function.