Abstract
In the present paper we are concerned with convergence in μ-density and μ-statistical convergence of sequences of functions defined on a subset D of real numbers, where μ is a finitely additive measure. Particularly, we introduce the concepts of μ-statistical uniform convergence and μ-statistical pointwise convergence, and observe that μ-statistical uniform convergence inherits the basic properties of uniform convergence.
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References
R. G. Bartle: Elements of Real Analysis. John Wiley & Sons, Inc., New York, 1964.
J. Connor: The statistical and strong p-Cesàro convergence of sequences. Analysis 8 (1988), 47-63.
J. Connor: Two valued measures and summability. Analysis 10 (1990), 373-385.
J. Connor: R-type summability methods, Cauchy criteria, P-sets and statistical convergence. Proc. Amer. Math. Soc. 115 (1992), 319-327.
J. Connor and M. A. Swardson: Strong integral summability and the Stone-Čech compactification of the half-line. Pacific J. Math. 157 (1993), 201-224.
J. Connor: A topological and functional analytic approach to statistical convergence. Analysis of Divergence. Birkhäuser-Verlag, Boston, 1999, pp. 403-413.
J. Connor and J. Kline: On statistical limit points and the consistency of statistical convergence. J. Math. Anal. Appl. 197 (1996), 393-399.
J. Connor, M. Ganichev and V. Kadets: A characterization of Banach spaces with separable duals via weak statistical convergence. J. Math. Anal. Appl. 244 (2000), 251-261.
K. Demirci and C. Orhan: Bounded multipliers of bounded A-statistically convergent sequences. J. Math. Anal. Appl. 235 (1999), 122-129.
H. Fast: Sur la convergence statistique. Colloq. Math. 2 (1951), 241-244.
J. A. Fridy: On statistical convergence. Analysis 5 (1985), 301-313.
J. A. Fridy and C. Orhan: Lacunary statistical convergence. Pacific J. Math. 160 (1993), 43-51.
J. A. Fridy and C. Orhan: Lacunary statistical summability. J. Math. Anal. Appl. vn173 (1993), 497-503.
J. A. Fridy and M. K. Khan: Tauberian theorems via statistical convergence. J. Math. Anal. Appl. 228 (1998), 73-95.
E. Kolk: Convergence-preserving function sequences and uniform convergence. J. Math. Anal. Appl. 238 (1999), 599-603.
I. J. Maddox: Statistical convergence in a locally convex space. Math. Proc. Cambridge Phil. Soc. 104 (1988), 141-145.
H. I. Miller: A measure theoretical subsequence characterization of statistical convergence. Trans. Amer. Math. Soc. 347 (1995), 1811-1819.
T. Šálat: On statistically convergent sequences of real numbers. Math. Slovaca 30 (1980), 139-150.
H. Steinhaus: Sur la convergence ordinaire et la convergence asymptotique. Colloq. Math. vn2 (1951), 73-74.
W. Wilczyński: Statistical convergence of sequences of functions. Real Anal. Exchange 25 (2000), 49-50.
A. Zygmund: Trigonometric Series. Second edition. Cambridge Univ. Press, Cambridge, 1979.
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Duman, O., Orhan, C. μ-Statistically Convergent Function Sequences. Czechoslovak Mathematical Journal 54, 413–422 (2004). https://doi.org/10.1023/B:CMAJ.0000042380.31622.39
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DOI: https://doi.org/10.1023/B:CMAJ.0000042380.31622.39