Functions with all singular sets of Hausdorff dimension bigger than one (Q910509)

In a generalized integration theory in higher dimensions recently developed by W. F. Pfeffer the following situation is typical: Given a function f of bounded variation on a set A of finite perimeter, one wishes to remove a small set S in such a way that certain Riemann-type sums of f on \(A\setminus S\) can be well approximated by a suitable primitive. The author constructs an example showing that such a set S often must have large Hausdorff dimension.