ON WITSENHAUSEN-KALAI CONSTANTS FOR EXTENSIONS OF THE SURFACE MEASURE ON S n

G. Pantsulaia; N.V. Zhivkov

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ON WITSENHAUSEN-KALAI CONSTANTS FOR EXTENSIONS OF THE SURFACE MEASURE ON S n

机译：关于维数在S n上扩展的维森豪森-卡莱常数

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It is proved that the sentence: "For a fixed n > 1 and for each extension A of the completion μ-n of the surface measure μn there is a Witsenhausen-Kalai constant w(nλ) for X " is independent from the theory ZF + DC, where ZF denotes Zermelo-Fraenkel system of axioms and DC denotes an axiom of dependent choice. If n = 2k, then we show that 1/2μ(Sn) is a Witsenhausen-Kalai constant for the family of all SO(n)-invariant extensions of μn, where SO(n) consists of all proper Euclidean isometries of Rn that fix the origin.

机译：证明以下句子：“对于固定n> 1且对于表面度量μn的完成度μ-n的每个扩展A，都有X的Witsenhausen-Kalai常数w（nλ）”独立于理论ZF + DC，其中ZF表示Zermelo-Fraenkel公理系统，DC表示从属选择公理。如果n = 2k，则表明对于μn的所有SO（n）不变扩展的族，1 /2μ（Sn）是Witsenhausen-Kalai常数，其中SO（n）由Rn的所有适当欧几里德等式组成，确定原点。

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《Algebras, groups and geometries》 |2010年第4期|p.391-407|共17页
作者
G. Pantsulaia; N.V. Zhivkov;
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P.O. Bo x 0175, 77 Kostava StreetDepartment of Mathematics, Georgian Technical University, Tbilisi, Georgia;

8 Acad. G. Bonchev Street, Institute of Mathematics and InformaticsBulgarian Academy of Sceinces, Sofia 1113, Bulgaria;

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ON WITSENHAUSEN-KALAI CONSTANTS FOR EXTENSIONS OF THE SURFACE MEASURE ON S n

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