On Some Density Topology with Respect to an Extension of Lebesgue Measure

Katarzyna Flak; Jacek Hejduk; Sylwia Tomczyk

doi:10.1515/tmmp-2017-0009

.blurhash-client-img { display: none !important; }

On Some Density Topology with Respect to an Extension of Lebesgue Measure

Tatra Mountains Mathematical Publications

Volume 68 (2017): Issue 1 (March 2017)

By: Katarzyna Flak, Jacek Hejduk and Sylwia Tomczyk

Open Access

|Nov 2017

Abstract

This paper presents a density type topology with respect to an extension of Lebesgue measure involving sequence of intervals tending to zero. Some properties of such topologies are investigated.

References

[1] KHARAZISHVILI, A. B.: A nonseparable extension of the Lebesgue measure without new nullsets, Real Anal. Exchange 33 (2007/2008), 259–268.10.14321/realanalexch.33.1.0259
Search in Google Scholar Back to article
[2] HEJDUK, J.—LORANTY, A.—WIERTELAK, R.: J-approximately continuous functions, Tatra Mt. Math. Publ. 62 (2015), 45–55.
Search in Google Scholar Back to article
[3] HEJDUK, J.—WIERTELAK, R.: On the abstract density topologies generated by lower and almost lower density operators, in: Traditional and present-day topics in real analysis (M. Filipczak et al., eds.), Łódź University Press, Łódź 2013, pp. 431–447.10.18778/7525-971-1.25
Search in Google Scholar Back to article
[4] HEJDUK, J.—WIERTELAK, R.: On the generalization of the density topologies on the real line, Math. Slovaca 64 (2014), 1267–1276.10.2478/s12175-014-0274-y
Search in Google Scholar Back to article
[5] HEJDUK, J.—WIERTELAK, R.: On some properties of J-approximately continuous functions, Math. Slovaca (to appear).
Search in Google Scholar Back to article
[6] MARCZEWSKI, E.: Sur l’extension de la measure lebesguienne, Fund. Math. 25 (1935), 551–558.10.4064/fm-25-1-551-558
Search in Google Scholar Back to article
[7] MARTIN, N. F. G.: Generalized condensation points, Duke Math. J. 28 (1961), 507–5014.
Search in Google Scholar Back to article
[8] OXTOBY, J. C.: Measure and Category, 2nd edition. Graduate Texts in Math. Vol. 2, Springer-Verlag, Berlin, 1980.10.1007/978-1-4684-9339-9
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.1515/tmmp-2017-0009 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

Journal RSS Feed

Language: English

Page range: 103 - 111

Submitted on: Feb 25, 2017

Published on: Nov 18, 2017

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

𝒥-density topologies,

𝒥-approximately continuous functions

Related subjects:

Mathematics,

General mathematics

© 2017 Katarzyna Flak, Jacek Hejduk, Sylwia Tomczyk, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 68 (2017): Issue 1 (March 2017)