Remarks on the Dirac δ-operator
Hans Ludwig Hamburger · Mathematical Proceedings of the Cambridge Philosophical Society · 1949
1. In this note we shall prove the Theorem 1. Let be a linear space of (real or complex) functions f(s) defined in the interval 0 ≤ s ≤ 1 subject to the following two conditions: (i) every function of the infinite sequence 1, s, s2, …, sn, … is an element of ; (ii) two elements, f(s) and g(s), of are to be considered as distinct if, and only if, they differ on a set of positive measure in the interval 0 ≤ s ≤ 1.