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PreprintCC BY 4.0arXiv

Exh subspaces of bounded variation spaces generated by submeasures

  • Jacek Gulgowski
  • Adam Kwela
  • Paweł Sawicki
  • Jacek Tryba
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Abstract

In the present paper we are building one more bridge between the theory of ideals on the set of natural numbers and the theory of spaces of functions of bounded variation. It is already known that Fσ ideals (that is, ideals of the form Fin(ϕ), where ϕ is a lower semicontinuous submeasure on ℕ) lead to a nice generalization of different concepts from the theory of functions of bounded variation (Waterman variation and Chanturya classes). In this paper we show that analytic P-ideals (that is, ideals of the form Exh(ϕ), where ϕ is a lower semicontinuous submeasure on ℕ) lead to a generalization of spaces of functions continuous in Λ-variation. The properties of this generalization are investigated.

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Cite

BibTeXRIS
BibTeX
@misc{gulgowski2026subspaces,
  title = {{Exh subspaces of bounded variation spaces generated by submeasures}},
  author = {Jacek Gulgowski and Adam Kwela and Paweł Sawicki and Jacek Tryba},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38891},
  eprint = {2610.38891},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38891},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Exh subspaces of bounded variation spaces generated by submeasures
AU  - Jacek Gulgowski
AU  - Adam Kwela
AU  - Paweł Sawicki
AU  - Jacek Tryba
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38891
UR  - https://arxiv.org/abs/2610.38891
AB  - In the present paper we are building one more bridge between the theory of ideals on the set of natural numbers and the theory of spaces of functions of bounded variation. It is already known that F_σ ideals (that is, ideals of the form Fin(ϕ), where ϕ is a lower semicontinuous submeasure on ℕ) lead to a nice generalization of different concepts from the theory of functions of bounded variation (Waterman variation and Chanturya classes). In this paper we show that analytic P-ideals (that is, ideals of the form Exh(ϕ), where ϕ is a lower semicontinuous submeasure on ℕ) lead to a generalization of spaces of functions continuous in Λ-variation. The properties of this generalization are investigated.
ER  -