Probabilities with Values in Scaled Hyperbolic Numbers

IF 1.2 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2025-06-15 DOI:10.1007/s00006-025-01394-7

Daniel Alpay, Ilwoo Cho

引用次数: 0

Abstract

In this paper, we introduce a notion of a probabilistic measure which takes values in t-scaled hyperbolic numbers for \(t\in \mathbb {R}\), with a system of axioms generalizing directly Kolmogorov’s axioms. i.e., we establish a suitable measure theory in the set \(\mathbb {D}_{t}\) of all t-scaled hyperbolic numbers for arbitrarily fixed \(t\in \mathbb {R}\).

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具有缩放双曲数值的概率

在本文中，我们引入了一个概率测度的概念，它取\(t\in \mathbb {R}\)的t尺度双曲数的值，并使用了一个直接推广Kolmogorov公理的公理系统。即，我们在任意固定\(t\in \mathbb {R}\)的所有t尺度双曲数集合\(\mathbb {D}_{t}\)中建立了一个合适的测度理论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Applied Clifford Algebras 数学-物理：数学物理

CiteScore

2.20

自引率

13.30%

发文量

审稿时长

3 months

期刊介绍： Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.