The Mackey–Zimmer theorem classifies ergodic group extensions $X$ of a measure-preserving system $Y$ by compact $K$, showing that such are isomorphic to skew-product $X \equiv Y \rtimes _\rho H$ for some closed subgroup $

Disclosures: T.C. Gascoyne: None. M.J. Petrak: None. J. Brandt: 5; Institutional Support: Smith & Nephew, DePuy Orthopaedics, Zimmer. 6; Material Support: Smith & Nephew, DePuy Orthopaedics. E.R. Bohm: 3B; Consultant payments from Smith & Nephew and DePuy Orthopaedics. 5; Institutional Support: Smith & Nephew, DePuy Orthopaedics, Zimmer. 6; Material Support: Smith & Nephew, DePuy Orthopaedics. ...

Stefan Kraut: Belebte Zimmer. Eine Dokumentation über das Anne-Sophie-Haus und den Würzburger Bau in Künzelsau. Künzelsau (Swiridoft) 2006. 208 S.

Abstract Furstenberg–Zimmer structure theory refers to the extension of dichotomy between compact and weakly mixing parts a measure-preserving dynamical system algebraic geometric descriptions such conditional setting, where is established relative factor analogs those are sought. Although unconditional characterizations known for arbitrary systems, situation understood under certain countabili...

Khush Mittal I read the paper by Chi et al. with interest. The authors found a greater hypoxia response gene expression in carcinomas than stromal cells grown in vitro, but were not sure of the underlying explanation (see Discussion in [1]). The underlying explanation may be the difference in mitotic activity and hence metabolic activity between these two cell types, such that hypoxia may be pr...

According to the Furstenberg-Zimmer structure theorem, every measure-preserving system has a maximal distal factor, and is weak mixing relative to that factor. Furstenberg and Katznelson used this structural analysis of measure-preserving systems to provide a perspicuous proof of Szemerédi’s theorem. Beleznay and Foreman showed that, in general, the transfinite construction of the maximal dista...