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Lineability within probability theory settings

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Conejero, Jose A. and Fenoy, Mar and Murillo Arcila, Marina and Seoane-Sepúlveda, Juan B. (2017) Lineability within probability theory settings. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, 111 (3). pp. 673-684. ISSN 15787303

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Official URL: http://link.springer.com/article/10.1007/s13398-016-0318-y


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Abstract

The search of lineability consists on finding large vector spaces of mathematical objects with special properties. Such examples have arisen in the last years in a wide range of settings such as in real and complex analysis, sequence spaces, linear dynamics, norm-attaining functionals, zeros of polynomials in Banach spaces, Dirichlet series, and non-convergent Fourier series, among others. In this paper we present the novelty of linking this notion of lineability to the area of Probability Theory by providing positive (and negative) results within the framework of martingales, random variables, and certain stochastic processes.


Item Type:Article
Uncontrolled Keywords:Lineability; Spaceability; Probability theory; Random variable; Stochastic process; Martingale
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:43790
Deposited On:05 Jul 2017 09:56
Last Modified:05 Jul 2017 11:37

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