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Science China Mathematics

, Volume 59, Issue 5, pp 921–934 | Cite as

Real-valued valuations on Sobolev spaces

Articles

Abstract

Continuous, SL(n) and translation invariant real-valued valuations on Sobolev spaces are classified. The centro-affine Hadwiger’s theorem is applied. In the homogeneous case, these valuations turn out to be L p -norms raised to p-th power (up to suitable multipication scales).

Keywords

Sobolev space valuation convex polytope 

MSC(2010)

46B20 46E35 52A21 52B45 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institut für Diskrete Mathematik und GeometrieTechnische Universität WienWienAustria

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