Abstract
To every pair of non-empty sets A, B ⊂ ℝn their (vector) Minkowski sum is defined by A + B = {a + b: a ∈ A, b ∈ B}. If A, B are compact sets (i.e. bounded closed sets), then A + B is compact. In this case each of the sets A, B, A + B necessarily has a volume (its Lebesgue measure). Denote these volumes by V(A), V(B), V(A + B).
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© 1988 Springer-Verlag Berlin Heidelberg
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Burago, Y.D., Zalgaller, V.A. (1988). The Brunn-Minkowski Inequality and the Classical Isoperimetric Inequality. In: Geometric Inequalities. Grundlehren der mathematischen Wissenschaften, vol 285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-07441-1_2
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DOI: https://doi.org/10.1007/978-3-662-07441-1_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05724-3
Online ISBN: 978-3-662-07441-1
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