子集上的加权 BS-Covering 维数的变分原理

数学物理学报 ›› 2026, Vol. 46 ›› Issue (6): 2106-2116.

子集上的加权 BS-Covering 维数的变分原理

张媛媛¹^,², 王蕴萍¹^,^*()

¹ 统计与数据科学学院, 宁波工程学院浙江宁波 315211
² 宁波大学数学与统计学院浙江宁波 315211

收稿日期:2025-08-11 修回日期:2026-01-04 出版日期:2026-12-26 发布日期:2026-08-14
通讯作者: 王蕴萍 E-mail:yunpingwangj@126.com
基金资助:
国家自然科学基金(12201328)

Variational Principle for Weighted BS-Covering Dimension on Subsets

Yuanyuan Zhang¹^,², Yunping Wang¹^,^*()

¹ School of Statistics and Data Science, Zhejiang Ningbo University of Technology
² Department of Mathematics, Ningbo University, Zhejiang Ningbo 315211

Received:2025-08-11 Revised:2026-01-04 Online:2026-12-26 Published:2026-08-14
Contact: Yunping Wang E-mail:yunpingwangj@126.com
Supported by:
NSFC(12201328)

摘要/Abstract

摘要：

该文定义了加权 BS-Covering 维数的概念, 并建立了加权 BS-Covering 维数的 Billingsley 定理和加权 BS-局部测度维数与加权 BS-Covering 维数之间变分原理.

关键词: 加权 BS-Covering 维数, Billingsley 定理, 变分原理.

Abstract:

In this paper, we introduce the concept of the weighted BS-Covering dimension and establish a Billingsley-type theorem for it. We also prove a variational principle relating the weighted BS-local measure dimension to the weighted BS-Covering dimension.

Key words: weighted BS-Covering dimension, Billingsley's theorem, variational principle.

中图分类号:

O192

张媛媛, 王蕴萍. 子集上的加权 BS-Covering 维数的变分原理[J]. 数学物理学报, 2026, 46(6): 2106-2116.

Yuanyuan Zhang, Yunping Wang. Variational Principle for Weighted BS-Covering Dimension on Subsets[J]. Acta mathematica scientia,Series A, 2026, 46(6): 2106-2116.

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