$\mu$-statistical convergence and the space of functions $\mu$-stat continuous on the segment

  • S.R. Sadigova Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan; Khazar University, Baku, Azerbaijan
Keywords: $\mu$-stat convergence, $\mu$-stat fundamentality, space of $\mu$-statistical continuous functions
Published online: 2021-10-04


In this work, the concept of a point $\mu$-statistical density is defined. Basing on this notion, the concept of $\mu$-statistical limit, generated by some Borel measure $\mu\left(\cdot \right)$, is defined at a point. We also introduce the concept of $\mu$-statistical fundamentality at a point, and prove its equivalence to the concept of $\mu$-stat convergence. The classification of discontinuity points is transferred to this case. The appropriate space of $\mu$-stat continuous functions on the segment with sup-norm is defined. It is proved that this space is a Banach space and the relationship between this space and the spaces of continuous and Lebesgue summable functions is considered.

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How to Cite
Sadigova S. $\mu$-Statistical Convergence and the Space of Functions $\mu$-Stat Continuous on the Segment. Carpathian Math. Publ. 2021, 13 (2), 433-451.