Superharmonic Functions in Brelot Spaces - Alakhrass, Mohammad
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We study superharmonic functions, reduced function, harmonic measures and Jensen measures in Brelot spaces. We introduce the concept of quasi multiply superharmonic functions on a product of Brelot spaces and study their properties. A main result obtained is characterizing the quasi superharmonic functions in terms of harmonic, finely harmonic and Jensen measures. Then we prove that a quasi multiply superharmonic function on a product of Brelot spaces equals its lower semicontinuous regularization out side of a 2-negligible set. Further we give a sufficient condition on a Brelot space under…mehr

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Produktbeschreibung
We study superharmonic functions, reduced function, harmonic measures and Jensen measures in Brelot spaces. We introduce the concept of quasi multiply superharmonic functions on a product of Brelot spaces and study their properties. A main result obtained is characterizing the quasi superharmonic functions in terms of harmonic, finely harmonic and Jensen measures. Then we prove that a quasi multiply superharmonic function on a product of Brelot spaces equals its lower semicontinuous regularization out side of a 2-negligible set. Further we give a sufficient condition on a Brelot space under which it becomes an extension space for superharmonic functions. As a result we characterize the extreme Jensen measures in such spaces. Finally we study extreme Jensen measures relative to several classes of multiply superharmonic functions.
Autorenporträt
Dr. Mohammad Alakhrass received his PhD in mathematics from McGill University in 2009.Since then he has published several articles in field of potential analysis. He is currently an assistant professor in the department of mathematics at the University of Sharjah.