## Rank one property for derivatives of functions with bounded variation.(English)Zbl 0791.26008

The basic result of this well organized and clearly written paper is contained in the following Theorem: Let $$\Omega$$ be an open subset of $$\mathbb{R}^ n$$, let $$u$$ be a function of bounded variation of $$\Omega$$ into $$\mathbb{R}^ m$$ and denote by $$D_ s u$$ the part of $$Du$$ which is singular with respect to Lebesgue measure. Then $$D_ s u$$ is a rank one measure and this means that for $$| D_ s u|$$ almost all $$x$$ the matrix $$[dD_ s u/d| D_ s u|](x)$$ has rank one.

### MSC:

 26B30 Absolutely continuous real functions of several variables, functions of bounded variation

### Keywords:

derivative; function of bounded variation; rank one measure
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### References:

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