Regulated functions. *-integral
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929357817118720 |
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| author | Derr, V. Ya. |
| author_facet | Derr, V. Ya. |
| contents | The present book gives a systematic overview of function theory and the theory of Stieltjes integral. In particular, we give a detailed account of the theory of functions of bounded variation and of the theory of regulated functions (= functions having finite one-sided limits at each point of their domain). We also present a detailed discussion of $σ$-continuous functions (= functions having at most countable set of points of discontinuity) and of the theory of Riemann-Stieltjes integral. We introduce the notion of *-integral, which allows us to integrate $σ$-continuous functions over functions of bounded variation. The limit theorems for *-integral are somewhat more convenient than their analogues for the general Lebesgue-Stieltjes integral. Some applications of *-integral are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12887 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regulated functions. *-integral Derr, V. Ya. Classical Analysis and ODEs The present book gives a systematic overview of function theory and the theory of Stieltjes integral. In particular, we give a detailed account of the theory of functions of bounded variation and of the theory of regulated functions (= functions having finite one-sided limits at each point of their domain). We also present a detailed discussion of $σ$-continuous functions (= functions having at most countable set of points of discontinuity) and of the theory of Riemann-Stieltjes integral. We introduce the notion of *-integral, which allows us to integrate $σ$-continuous functions over functions of bounded variation. The limit theorems for *-integral are somewhat more convenient than their analogues for the general Lebesgue-Stieltjes integral. Some applications of *-integral are also discussed. |
| title | Regulated functions. *-integral |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2405.12887 |