On the exceptional sets of the flux of a bounded vectorfield. (English) Zbl 1042.49039
Summary: For each purely \(n-1\) unrectifiable compact set \(C \subset \mathbb R^n\) such that \(0 < \mathcal H^{n-1}(C) < \infty\), there is a bounded Borel measurable vectorfield \(v: \mathbb R^n\to \mathbb R^n\) whose flux vanishes in \(\mathbb R^n \sim C\) but not in \(\mathbb R^n\)
MSC:
| 49Q15 | Geometric measure and integration theory, integral and normal currents in optimization |
| 28A75 | Length, area, volume, other geometric measure theory |
| 26A39 | Denjoy and Perron integrals, other special integrals |
| 26B15 | Integration of real functions of several variables: length, area, volume |
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