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On $ \mu$-statistical convergence


Authors: B. T. Bilalov and S. R. Sadigova
Journal: Proc. Amer. Math. Soc. 143 (2015), 3869-3878
MSC (2010): Primary 40A05, 26A15, 11B05
DOI: https://doi.org/10.1090/S0002-9939-2015-12528-2
Published electronically: February 26, 2015
MathSciNet review: 3359578
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Abstract: The concept of $ \mu $-statistical convergence at a point for measurable functions in measurable space with a measure is introduced in this work. This concept is a generalization of a similar idea about the sequence of numbers. We also introduce the concept of $ \mu $-statistical fundamentality at a point, and the equivalence of these two concepts is proved. The concept of $ \mu $-statistical convergence at a point generalizes the usual one of the limit of a function at a point.


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Additional Information

B. T. Bilalov
Affiliation: Department of Non-harmonic Analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, B. Vahabzadeh 9, Baku, Azerbaijan Republic, AZ1141
Email: b_bilalov@mail.ru

S. R. Sadigova
Affiliation: Department of Non-harmonic Analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, B. Vahabzadeh 9, Baku, Azerbaijan Republic, AZ1141
Email: s_sadigova@mail.ru

DOI: https://doi.org/10.1090/S0002-9939-2015-12528-2
Keywords: Statistical convergence, statistical fundamentality, statistical continuity
Received by editor(s): July 28, 2013
Received by editor(s) in revised form: April 21, 2014
Published electronically: February 26, 2015
Communicated by: Sergei K. Suslov
Article copyright: © Copyright 2015 American Mathematical Society