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Difference between revisions of "User:Boris Tsirelson/sandbox2"

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and the following identity  holds:
 
and the following identity  holds:
 
\begin{equation}\label{e:area_formula}
 
\begin{equation}\label{e:area_formula}
\int_A J f (y) \, dy = \int_{\mathbb R^m} \mathcal{H}^0  (A\cap f^{-1} (\{z\}))\,  d\mathcal{H}^n (z)\, .
+
\int_A J f (y) \, dy = \int_{\mathbb R^m} \mathcal{H}^0  (A\cap f^{-1} (\{z\}))\,  d\mathcal{H}^n (z)\, .
 
\end{equation}
 
\end{equation}
  

Revision as of 06:05, 21 July 2013

and the following identity holds: \begin{equation}\label{e:area_formula} \int_A J f (y) \, dy = \int_{\mathbb R^m} \mathcal{H}^0 (A\cap f^{-1} (\{z\}))\, d\mathcal{H}^n (z)\, . \end{equation}

Cp. with 3.2.2 of [EG]. From \eqref{e:area_formula} it is not difficult to conclude the following generalization (which also goes often under the same name):



\begin{equation}\label{ab} E=mc^2 \end{equation} By \eqref{ab}, it is possible. But see \eqref{ba} below: \begin{equation}\label{ba} E\ne mc^3, \end{equation} which is a pity.

How to Cite This Entry:
Boris Tsirelson/sandbox2. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Boris_Tsirelson/sandbox2&oldid=29987