The Oscillation of an Operator on L p

On the Representation of Order Continuous Operators by Random Measures

“…Now we fix some notations and recall some definitions. Let (X, sé, p) and (Y, 38, v) always be measure spaces where X and Y are separable metric spaces and se, 38 are their a-algebras of Borel sets, such that (X, sé) and (Y, 3d) are standard measure spaces [37,Chapter V,§2]. p and v always stand for strictly positive and finite measures, d denotes the metric on X or Y, and d(A) is the diameter of a subset of Xor Y.…”