Difference between revisions of "User:Boris Tsirelson/sandbox2"
From Encyclopedia of Mathematics
| Line 1: | Line 1: | ||
| − | 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 05:45, 12 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=29922
Boris Tsirelson/sandbox2. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Boris_Tsirelson/sandbox2&oldid=29922