References
- [1] BUCK, R. C.: The measure theoretic approach to density, Amer. J. Math. 68 (1946), 560–580.10.2307/2371785
- [2] CRISTEA, LIGIA L.—PAŠTÉKA, M.: Uniform distribution with respect to density, Unif. Distrib. Theory 12, (2017), no. 1, 123–138.10.1515/udt-2017-0008
- [3] DRMOTA, M., TICHY, R. F.: Sequences, Discrepancies and Applications. Springer-Verlag, Berlin, 1997.10.1007/BFb0093404
- [4] ERDÖS, P.: On the density of some sequences of numbers II, J. London Math. Soc. 12 (1937), 7–11.10.1112/jlms/s1-12.45.7
- [5] FAST, H.: Sur la convergence statistique, Coll. Math. 2 (1951), 241–244.10.4064/cm-2-3-4-241-244
- [6] GREKOS, G.: On various definitions of density (a survey), Tatra Mt. Math. Publ. 31 (2005), 17–27.
- [7] GREKOS, G.: The density set (a survey), Tatra Mt. Math. Publ. 31 (2005), 103–111.
- [8] GRABNER, P. J.—STRAUCH, O.—TICHY, R. F.: Lp-discrepancy and statistical independence of sequences, Czechoslovak Math. J. 49 (1999), no. 1, 97–110.10.1023/A:1022460225387
- [9] GRABNER, P. J.—TICHY, R. F.: Remark on statistical independence of sequences, Math. Slovaca, 44 (1994), no. 1, 91–94.
- [10] HLAWKA, E.: Folgen auf kompakten Räumen, Abh. Math. Semin. Univ. Hamburg. 20 (1956), 223–241.10.1007/BF03374560
- [11] HLAWKA, E.: Theorie der Gleichverteilung. [Theory of uniform distribution] Bibliographisches Institut, Mannheim-Wien-Zrich, 1979.
- [12] HORBOWICZ, J.: Criteria for uniform distribution Indag. Math. 43, 1987, 301–307.10.1016/1385-7258(81)90041-X
- [13] IACO, M. R.—PASTEKA, M.—TICHY R. F.: Measure density for set decompositions and uniform distribution, Rend. Circ. Math. Palermo 64 (2015), no. 2, 323–339.10.1007/s12215-015-0202-1
- [14] KUIPERS, L.—NIEDERREITER, H.: Uniform Distribution of Sequences. John Wiley and Sons, N.Y, London, Sydney, Toronto, 1974.
- [15] KOSTYRKO, P.—MÁČAJM.—ŠALÁT, T.—STRAUCH, O.: On statistical limit points. Proc. Am. Math. Soc. 129 (2001), no. 9, 2647–2654.10.1090/S0002-9939-00-05891-3
- [16] NOVOSELOV, E. V.: Topological theory of polyadic numbers, Trudy Tbilis. Mat. Inst. 27 (1960), 61–69. (In Russian)
- [17] NOVOSELOV, E. V.: New method in the probability number theory, Doklady Akad. Nauk. Ser. Mat. 28 (1964), no. 2, 307–364. (In Russian)
- [18] NARKIEWICZ, W.: Teoria Liczb. PWN, Warszawa, 1991. (In Polish)
- [19] NIVEN, I.: Uniform distribution of sequences of integers, Trans. Amer. Math. Soc. 98 (1961) 52–61.10.1090/S0002-9947-1961-0120214-8
- [20] PARTHASARATHY, K. R.: Probability Measures on Metric Spaces. Academic Press, New York, London, 1967.10.1016/B978-1-4832-0022-4.50006-5
- [21] PAŠTÉKA, M.: Some properties of Buck’s measure density, Math. Slovaca 42 (1992), no. 1, 15–32.
- [22] PAŠTÉKA, M.: Remarks on one type of uniform distribution Unif. Distrib. Theory 2 (2007), no. 1, 79–92.
- [23] PAŠTÉKA, M.: On four approaches to density. Spectrum Slovakia Vol. 3. Peter Lang; Frankfurt am Main; VEDA, Bratislava, 2014.
- [24] PAŠTÉKA, M.: Remarks on Buck’s measure density, Tatra Mt. Math. Publ. 3 (1993), 191–200.
- [25] PAŠTÉKA, M.: Density and related topics. VEDA, Publishing House of the Slovak Academy of Sciences, Bratislava, 2017.
- [26] PAŠTÉKA, M.: Central limit theorem and the distribution of sequences, Tatra Mt. Math. Publ. 77 (2020), 43–52.10.2478/tmmp-2020-0031
- [27] PAŠTÉKA, M.: Remarks on continuously distributed sequences, Carpat. Mathem. Publ. 13 (2021), no. 1, 89–97.10.15330/cmp.13.1.89-97
- [28] PASTEKA, M.—TICHY, R.: A note on the correlation coefficient of arithmetic functions, Acta Acad. Paed. Agriensis, Sectio Mathematicae 30 (2003), 109–114.
- [29] PASTEKA, M.—TICHY, R.: Measurable sequences, Riv. Mat. Univ. Parma, 10 (2019), 63–84.
- [30] RAUZY, G.: Proprietes statistique de suites arithmetiques. Le Mathematicien. Vol. li. Collection SUP, Presses Universitaires de France, Paris, 1976.
- [31] ŠALÁT, T.: On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139–150.
- [32] SCHOENBERG, I.: Über die asymptotische Verteilung reeler Zahlen (mod 1), Math. Z. 28 (1928), no. 1, 171–199.10.1007/BF01181156
- [33] STRAUCH, O.: Distribution of Sequences a Theory. VEDA, Publishing House of the Slovak Academy of Sciences, Bratislava; Academia, Centre of Administration and Operations of the CAS, Prague, 2019.
- [34] STRAUCH, O.—PORUBSKÝ, Š.: Distribution of Sequences: a sampler, In: Schriftenreihe der Slowakischen Akademie der Wissenschaften [Series of the Slovak Academy of Sciences], Vol. 1, Peter Lang, Frankfurt am Main, 2005.
- [35] TICHY, R. F.: A criterion for the uniform distribution of sequences in compact metric spaces, Rend. Circ. Mat. Palermo 36 (1987), 332–342.10.1007/BF02843743
- [36] WEYL, H.: Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann, 77 (1916), 313–352.10.1007/BF01475864