The proof of the Brunn Minkowski inequality predates modern measure theory; the development of measure theory and Lebesgue integration allowed connections to be made between geometry and analysis, to the extent that in an integral form of the Brunn Minkowski inequality known as the Pr�kopa Leindler inequality the geometry seems almost entirely absent.
12.
The proof of the Brunn Minkowski inequality predates modern measure theory; the development of measure theory and Lebesgue integration allowed connections to be made between geometry and analysis, to the extent that in an integral form of the Brunn Minkowski inequality known as the Pr�kopa Leindler inequality the geometry seems almost entirely absent.
13.
One can show that the Brunn Minkowski inequality for convex bodies in "'R " "'n " implies Minkowski's first inequality for convex bodies in "'R " "'n ", and that equality in the Brunn Minkowski inequality implies equality in Minkowski's first inequality.
14.
One can show that the Brunn Minkowski inequality for convex bodies in "'R " "'n " implies Minkowski's first inequality for convex bodies in "'R " "'n ", and that equality in the Brunn Minkowski inequality implies equality in Minkowski's first inequality.
