ON A SPACE OF μ-STATISTICAL CONTINUOUS FUNCTIONS - Sadigova, Sabina R.; Hasanli, Raziyya R.; Karacam, Cemil (INST MATHEMATICS & MECHANICS, NATL ACAD SCIENCES AZERBAIJAN, 2018)
The concepts of mu-statistical discontinuities of the first and second kinds for functions in some measurable space with the measure mu are introduced in this work. The space of mu-statistical continuous functions on some interval is considered, some properties of functions in this space are studied. The relationship between this space and the spaces of continuous and Lebesgue-summable functions in the case where mu is a Lebesgue measure is also considered.
Keywords: mu-statistical discontinuities; mu-statistical continuity; the space of mu-statistical continuous functions; POSITIVE LINEAR-OPERATORS; IDEAL CONVERGENCE; SEQUENCES; APPROXIMATION; SUMMABILITY; THEOREMS; Mathematics