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Suppose $\phi:\mathbb{R}^n \rightarrow \mathbb{R}$ is smooth, $Z=\{x: \phi(x)=0\}$ and $D\phi\neq0$ on $Z$. Is anyone familiar with use of the notation $dZ$ for the measure $$\sum_{x \in Z} |D\phi(x)|\delta_x,$$ where $\delta_x$ is the Dirac measure at $x$? If so, can you explain it?

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    Does $f = \phi$?2011-06-26
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    Regarding your first question, I am not (familiar with this notation). Do you have any reference?2011-06-26
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    Just not to be confused: if smooth means just $C^\infty$?2011-06-26

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