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Lineability within probability theory settings

  • J. Alberto Conejero
  • Mar Fenoy
  • Marina Murillo-Arcila
  • Juan B. Seoane-Sepúlveda
Original Paper
  • 135 Downloads

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.

Keywords

Lineability Spaceability Probability theory Random variable Stochastic process Martingale 

Mathematics Subject Classification

46E10 46E99 60B11 

Notes

Acknowledgments

This work was partially supported by Ministerio de Educación, Cultura y Deporte, projects MTM2013-47093-P and MTM2015-65825-P, by the Basque Government through the BERC 2014-2017 program and by the Spanish Ministerio de Economía y Competitividad: BCAM Severo Ochoa excellence accreditation SEV-2013-0323.

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Copyright information

© Springer-Verlag Italia 2016

Authors and Affiliations

  1. 1.Instituto Universitario de Matemática Pura y Aplicada (IUMPA)Universitat Politècnica de ValènciaValenciaSpain
  2. 2.Departamento de Estadística e Investigación Operativa, Facultad de Ciencias MatemáticasUniversidad Complutense de MadridMadridSpain
  3. 3.BCAM-Basque Center for Applied MathematicsBilbaoSpain
  4. 4.Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM)MadridSpain
  5. 5.Departamento de Análisis Matemático, Facultad de Ciencias MatemáticasUniversidad Complutense de MadridMadridSpain

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