Leibniz seminorms in probability spaces
Adam Besenyei, Zoltan Leka
TL;DR
This paper investigates the Leibniz property of centered moments in probability spaces, addressing a question about the non-commutative standard deviation and its mathematical properties.
Contribution
It provides new insights into the Leibniz property of centered moments and answers a specific open question regarding non-commutative standard deviation.
Findings
Centered moments satisfy the strong Leibniz property under certain conditions
The non-commutative standard deviation exhibits specific Leibniz behavior
The paper clarifies the mathematical structure of moments in probability spaces
Abstract
In this paper we study the (strong) Leibniz property of centered moments of bounded random variables. We shall answer a question raised by M. Rieffel on the non-commutative standard deviation.
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