In some spaces of differentiable functions, the finitely generated ideals which are closed are characterized in terms of the zeros of the generators. Applications are made to problems of division for ...

We develop a partitioning lemma (see Lemma 5) for superadditive set functions satisfying certain continuity conditions. This leads to a relatively simple proof of two theorems of A. S. Besicovitch on ...

Harmonic functions, defined as twice continuously differentiable functions satisfying Laplace’s equation, have long been a subject of intense study in both pure and applied mathematics. Their ...