Nilspace Factors for General Uniformity Seminorms, Cubic Exchangeability and Limits

We study a class of measure-theoretic objects that we call

Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Candela, Pablo, Szegedy, Balázs
Format: E-Book Buch
Sprache:Englisch
Veröffentlicht: Providence, Rhode Island American Mathematical Society 2023
Ausgabe:1
Schriftenreihe:Memoirs of the American Mathematical Society
Schlagworte:
Curves, Cubic
Measure-preserving transformations
Nilpotent groups
ISBN:1470465485, 9781470465483
ISSN:0065-9266, 1947-6221
Online-Zugang:Volltext
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Inhaltsangabe:
  • Introduction -- Measure-theoretic preliminaries -- Cubic couplings -- The structure theorem for cubic couplings -- On characteristic factors associated with nilpotent group actions -- On cubic exchangeability -- Limits of functions on compact nilspaces -- Background results from measure theory
  • Cover -- Title page -- Chapter 1. Introduction -- Acknowledgments -- Chapter 2. Measure-theoretic preliminaries -- 2.1. Some basic notions -- 2.2. Couplings -- 2.3. Closed properties in a coupling space -- 2.4. Localization -- 2.5. Conditional independence in set lattices -- 2.6. Idempotent couplings -- Chapter 3. Cubic couplings -- 3.1. Conditional independence of simplicial sets -- 3.2. Tricubes -- 3.3. ^{ }-convolutions and ^{ }-seminorms associated with a cubic coupling -- 3.4. Fourier -algebras -- 3.5. Properties of ^{ }-convolutions -- 3.6. Topologization of cubic couplings -- 3.7. Continuous ⁿ-convolutions -- 3.8. Topological nilspace factors of \ns -- Chapter 4. The structure theorem for cubic couplings -- 4.1. Verifying the ergodicity and composition axioms -- 4.2. Complete dependence of corner couplings -- 4.3. Convolution neighbourhoods -- 4.4. Construction of the coupling Υ. -- 4.5. Verifying the corner-completion axiom -- Chapter 5. On characteristic factors associated with nilpotent group actions -- Chapter 6. On cubic exchangeability -- Chapter 7. Limits of functions on compact nilspaces -- Appendix A. Background results from measure theory -- Bibliography -- Back Cover