•  
  •  
 

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Abstract

In the paper we investigate maps between idempotent measures spaces, τ-maxitive idempotent measures and their extensions and restrictions. For an idempotent measure we prove that its extension is τ-maxitive if and only if its restriction is τ-maxitive.

First Page

162

Last Page

172

References

1. Eshimbetov M.R. Luzin measurable functions and idempotent τ-smooth measures (Russian). Bulletin of the Institute of Mathematics, Vol. 7, No. 2, 136-142 (2021).

2. Eshimbetov M.R. On extensions and restrictions of τ-maxitive idempotent measures. Uzbek Mathematical Journal, Vol. 65, Issue 3, 71-80 (2021).

3. Fedorchuk V.V., Sadovnichii Yu.V. On some topological and categorical properties of measures with alternating signs (Russian). Fundam. Prikl. Mat., Vol. 23, Issue 5, No. 2, 597-618 (1999).

4. Gunawardena J. Idempotency, Publ. of the Newton Institute. Vol. 11 (1998), Cambridge University Press, Cambridge, (Online publication date: May 2010).

5. Kolokoltsov V.N., Maslov V.P. Idempotent analysis and its applications. Kluwer Publishing House. Vol. 401 (1997).

6. Litvinov G.L., Maslov V.P. Idempotent Mathematics and Mathematical Physics, Contemporary Mathematics. Vol. 370 (2005).

7. Puhalskii A. Large deviations and idempotent probability. Chapman & Hall/CRC. Vol. 500 (2001).

8. Zaitov A.A. On a metric on the space of idempotent probability measures. Applied General Topology, Vol. 16, Issue 1, 35-51 (2020).

9. Zaitov A.A., Ishmetov A.Ya. On monad generating by the functor I β , Vestnik of National University of Uzbekistan. No 2, 61–64 (2013).

10. Zaitov A.A., Ishmetov A.Ya. Homotopy Properties of the Space If(X) of Idem-potent Probability Measures, Math. Notes, Vol. 106: 3-4, 562–571 (2019).

11. Zarichnyi M. Spaces and mappings of idempotent measures. Izvestiya: Math. Vol. 74, Issue 3, 45-64 (2010).

12. Zarichnyi M., Bazylevych L., Repovs D. Spaces of idempotent measures of compact metric spaces. Topology Appl. Vol. 157, Issue 1, 136–144 (2010).

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.