Symmetric seminorms and the Leibniz property

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:452

Article

Leka, Zoltan¹ 

[1] Royal Holloway Univ London, Egham Hill, Surrey TW20 0EX, England

关键词: Standard deviation;    Central moments;    Leibniz inequality;    Symmetric norm;    Derivation;   

DOI  :  10.1016/j.jmaa.2017.02.070

来源: Elsevier

【 摘 要 】

We show that certain symmetric seminorms on R-n satisfy the Leibniz inequality. As an application, we obtain that L-p norms of centered bounded real functions, defined on probability spaces, have the same property. Even though this is well-known for the standard deviation it seems that the complete result has never been established. In addition, we shall connect the results with the differential calculus introduced by Cipriani and Sauvageot and Rieffel's non-commutative Riemann metric. (C) 2017 Published by Elsevier Inc.

【 授权许可】

Free