Hölder’s Generalized Inequality on the Space of Upper Semi-Continuous Functions
DOI:
https://doi.org/10.58649/3b3yr385Keywords:
idempotent measure, max-plus linear functional, Borel sets, upper semi continuous functionsAbstract
For a compact Hausdorff space X, we consider the space of set-functions on the σ-algebra of the Borel subsets of X, and also the space of normalized max-plus linear functionals on the space USC(X) of upper semi-continuous functions on X, equipped with idempotent operations. The main result establishes that a max-plus version of the Hölder inequality holds on the space of upper semi-continuous functions.
References
Sh.A. Ayupov, M.R. Eshimbetov, A.A. Zaitov, Hölder inequality on the space of upper semi-continuous functions, Eurasian Mathematical Journal, 17(1) (2026), 10–22.
V.I. Bogachev, Measure Theory. Vol. I, Springer, (2007).
V.I. Bogachev, Measure Theory. Vol. II, Springer, (2007).
R. Engelking, General Topology, Revised and completed edition. Berlin: Heldermann Verlag, (1989).
J. Gunawardena, (Ed.) Idempotency, Publications of the Newton Institute, Cambridge University Press, Cambridge, 11 (1998).
L.D.R. Kočinac, A.A. Zaitov, M.R. Eshimbetov, On the Čech-completeness of the space of τ-smooth idempotent measures, Axioms, 13(8) (2024), 569–582.
L.D.R. Kočinac, A.A. Zaitov, M.R. Eshimbetov, On the spaces of idempotent probability measures on superparacompact spaces, Mat. Vesnik, in press.
B. Makarov, A. Podkorytov, Real Analysis: Measures, Integrals and Applications, Springer-Verlag London, (2013).
A. Puhalskii, Large Deviations and Idempotent Probability, Chapman & Hall/CRC, (2001).
T. Radul, Idempotent measures: absolute retracts and soft maps. Topological Methods in Nonlinear Analysis, 56(1) (2020), 161–172.
A. Sheldon, Measure, Integration and Real Analysis, Springer Open, (2010).
V.S. Varadarajan, Measures on topological spaces, Matematicheskii Sbornik, 55 (1961), 35–100.
A.A. Zaitov, M.R. Eshimbetov, On a max-plus variant of the Riesz representation theorem, Bulletin of the Institute of Mathematics, 6(5) (2023), 73–79.
M. Zarichnyi, Spaces and mappings of idempotent measures, Izvestiya: Mathematics, 74(3) (2010), 445–464.
M. Zarichnyi, L. Bazylevych, D. Repovš, Spaces of idempotent measures of compact metric spaces, Topology and its Applications, 157(1) (2010), 136–144.
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