Normed modules, integral sequences, and integrals with variable upper limits

Autor:	Liu, Miantao, Liu, Yu-Zhe, Liu, Shengda
Rok vydání:	2024
Předmět:	Mathematics - Category Theory Mathematics - Classical Analysis and ODEs 16D10 16G10 46H25
Druh dokumentu:	Working Paper
Popis:	This paper introduces a novel framework for categorizing the Lebesgue integral with variable upper limits, utilizing normed modules over finite-dimensional $k$-algebras $\mathit{\Lambda}$ and the category $\mathscr{A}^p$ of $\mathit{\Lambda}$. We redefine the integration process by incorporating integral partial ordered set, which provide a categorification of integral with variable upper limits. Moreover, we provide two applications for this categorification in Chapters 5 and 6. Comment: 32 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2411.19904 Zobrazit plný text záznamu View this record from Arxiv