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Geometric Aspects of Functional Analysis pp 71–105Cite as

Valuations on the Space of Quasi-Concave Functions

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2169))

Abstract

We characterize the valuations on the space of quasi-concave functions on \(\mathbb{R}^{N}\), that are rigid motion invariant and continuous with respect to a suitable topology. Among them we also provide a specific description of those which are additionally monotone.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Informatica “U. Dini”, Viale Morgagni 67/A, 50134, Firenze, Italy

    Andrea Colesanti & Nico Lombardi

Authors
  1. Andrea Colesanti
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  2. Nico Lombardi
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Corresponding author

Correspondence to Andrea Colesanti .

Editor information

Editors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, Tel-Aviv, Israel

    Bo'az Klartag

  2. Mathematics Department, Technion - Israel Institute of Technology, Haifa, Israel

    Emanuel Milman

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Colesanti, A., Lombardi, N. (2017). Valuations on the Space of Quasi-Concave Functions. In: Klartag, B., Milman, E. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2169. Springer, Cham. https://doi.org/10.1007/978-3-319-45282-1_6

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