Measure filters: An extension of Wiener's theorem

We present an extension of Wiener's theorem, a nonlinear filter called the measure filter which, when applied to a measure, filters out all but the lowest dimensional part of that measure. We also extend the work of Strichartz in the case of codimension one, for functions of bounded variation, by allowing for a wide range of kernels which can be used to extract the jump part of the distributional derivative of a BV function. Our method of proof is different from that of Wiener and Strichartz.