Duality and the Kestelman-Borwein-Ditor theorem

We deduce both the measure and the category cases of the theorem in the title from one category theorem, using the density topology for the first and the usual Euclidean topology for the second. We also obtain a unified proof for the Uniform Convergence Theorem for slowly varying functions.

en

http://eprints.lse.ac.uk/6841/