2018/05/28 by Ignacio S. Gomez
Computer Science · Mathematics · Physics and Astronomy · #Advanced Algebra and Logic #Advanced Mathematical Theories and Applications #Formalism (music) #Generalization #Limit (mathematics) #Property (philosophy) #Set (abstract data type) #Statistical Mechanics and Entropy #math-ph #math.MP
paper · pdf · doi:10.1016/s0034-4877(19)30023-0
arxiv created 2018/05/28 · openalex created_date 2018/06/13 · openalex publication_date 2019/03/01 · arxiv updated 2019/03/27 · openalex updated_date 2026/08/05
We address a generalization of the Vitali set through a deformed translational property that stems from a generalized algebra derived from the nonextensive statistics. The generalization is based on the so-called q-addition x⊕q y=x+y+(1-q)xy for rational values of q, where the ordinary formalism is recovered when the control parameter q → 1. The generalized Vitali set is non-measurable for all rational parameter (1)/(2)<q≤1, but in the limit q→(1)/(2) the non-measurability cannot be guaranteed. Furthermore, assuming measurability when q→(1)/(2), then this must be positive.