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Published in:
2016 | OriginalPaper | Chapter
10. Quasiconcave Functions
Authors : Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
Published in: Foundations of Symmetric Spaces of Measurable Functions
Publisher: Springer International Publishing
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Abstract
In this chapter we study quasiconcave functions in conjunction with fundamental functions of symmetric spaces. We show that every concave function is also quasiconcave, and conversely, for every quasiconcave function V, there exists its least concave majorant \(\widetilde{V }\), satisfying inequality \(\frac{1} {2}\widetilde{V } \leq V \leq \widetilde{ V }\). We also show that fundamental functions of symmetric spaces are quasiconcave.