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?
Notation for a certain kind of discrete measure
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calculus
measure-theory
multivariable-calculus
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0Just not to be confused: if smooth means just $C^\infty$? – 2011-06-26