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Fatou’s lemma for Sugeno integral |
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| Authors: | Hamzeh Agahi A Flores-Franuli? S Mansour Vaezpour |
| Institution: | a Department of Statistics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424, Hafez Ave., Tehran 15914, Iran b Statistical Research and Training Center, Tehran, Iran c Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile d Department of Mathematics and Computer Science, Amirkabir University of Technology, 424, Hafez Ave., Tehran 15914, Iran |
| Abstract: | Fatou’s lemma plays an important role in classical probability and measure theory. Non-additive measure is a generalization of additive probability measure. Sugeno’s integral is a useful tool in several theoretical and applied statistics which have been built on non-additive measure. In this paper, a Fatou-type lemma for Sugeno integral is shown. The studied inequality is based on the classical Fatou lemma for Lebesgue integral. To illustrate the proposed inequalities some examples are given. |
| Keywords: | Sugeno integral Non-additive measure Monotone function Fatou&rsquo s lemma Applied statistics |
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