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Convex Bodies: The Brunn–Minkowski Theory, Second Edition by Rolf Schneider

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3

Minkowski addition

3.1 Minkowski addition and subtraction

The aim of this chapter is a more systematic study of Minkowski addition. In the present section we first collect some elementary formal properties of this addition and then investigate its convexifying effect. After that, we introduce a certain coun -terpart to Minkowski addition, a useful operation that has been called Minkowski subtraction.

The sum of two subsets image was defined by

image

and the scalar multiple by

for real numbers λ. One may rewrite the definition of the sum in the form

This ...

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