Uniform Distribution with Respect to Density

BINDER, C.: Über einen Satz von de Bruijn und Post, ¨Osterr. Akad. Wiss. Math.-Naturw. Kl. SB. II, 179 (1971), 233-251.Search in Google Scholar

DE BRUIJN, N.G.-POST, K. A.: A remark on uniformly distributed sequences and Riemann integrability Indag. Math. 30 (1968), 149-150.Search in Google Scholar

BUCK, R. C.: The measure theoretic approach to density, Amer. J. Math 68 (1946), 560-580.10.2307/2371785Search in Google Scholar

CRISTEA, L. L.-PRODINGER, H.: Moments of distributions related to digital expansions, J. Math. Anal. Appl. 315 (2006), 606-625.10.1016/j.jmaa.2005.05.043Search in Google Scholar

CRISTEA, L. L.-TICHY, R. F.: Discrepancies of point sequences on the Sierpi´nski carpet, Math. Slovaca, 53 (2003), no. 4, 351-367.Search in Google Scholar

DRMOTA, M.-TICHY, R.F.: Sequences, Discrepancies and Applications. Springer- -Verlag, Berlin Heidelberg, 1997.10.1007/BFb0093404Search in Google Scholar

FALCONER, K. J.: Fractal Geometry. Mathematical Foundations and Applications. John Wiley & Sons, Chichester, 1990.10.2307/2532125Search in Google Scholar

HEDRLIN, Z.: On integration in compact metric spaces, Comment. Math. Univ. Carolinae, 2 4 (1961), no. 4, 17-19.Search in Google Scholar

HLAWKA, E.: Theorie der Gleichverteilung. Bibliographisches Institut, Mannheim, 1979.Search in Google Scholar

IACO, M.R.-PAŠTÉKA, M.- TICHY, R. F.: Measure density for set decompositions and uniform distribution, Rend. Circ. Math. Palermo 2 (2015), 323-339.10.1007/s12215-015-0202-1Search in Google Scholar

KUIPERS, L.-NIEDERREITER, H.: Uniform Distribution of Sequences. John Wiley and Sons, N.Y. London, Sydney, Toronto, 1974.Search in Google Scholar

NOVOSELOV, E.V.: Topological theory of polyadic numbers, Trudy Tbilis. Mat. Ist. 27 (1960), 61-69. (In Russian) Search in Google Scholar

New method in the probability number theory, Doklady Akad. Nnauk. Ser. Matem. 28 (1964), no. 2, 307-364. (In Russian)Search in Google Scholar

OKADA, T.-SEKIGUCHI, T.-SHIOTA, Y.: Applications of binomial measures to power sums of digital sums, J. Number Theory 52 (1995), 256-266. 10.1006/jnth.1995.1068Search in Google Scholar

A generalization of Hata-Yamaguti’s results on the Takagi function II: Multinomial case, Japan J. Indust. Appl. Math. 13 (1996), 235-463.10.1007/BF03167257Search in Google Scholar

PAŠTÉKA, M.: On Four Approaches to Density. VEDA, Bratislava, ISBN 978-80- -224-1327-5; Peter Lang, Frankfurt am Main, ISBN 978-3-631-64941-1, 2013.Search in Google Scholar

Remarks on one type of uniform distribution, Unif. Distrib. Theory 2 (2007), no. 1, 79-92.Search in Google Scholar

PAŠTÉKA, M.-ŠAL´AT, T.: Buck’s measure density and sets of positive integers containing arithmetic progressions, Math. Slovaca 41 (1991), 283-293.Search in Google Scholar

PAŠTÉKA, M.-PORUBSK´Y, V S.: On the distribution of sequences of integers, Math. Slovaca 43 (1993), 521-639.Search in Google Scholar

PAŠTÉKA, M.-TICHY, R. F.: Distribution Problems in Dedekind Domains and Submeasures, Annali dell’ Universita di Ferrara, Sezione VII-Scienze Matematiche 40 (1994), 191-206.Search in Google Scholar

STRAUCH, O-PORUBSK´Y, Š.: Distribution of Sequences: A Sampler. Peter Lang, SAV, Frankfurt am Main, 2005.Search in Google Scholar

TICHY, R. F.-WINKLER, R.: Uniform distribution preserving mappings, Acta. Arith. 60 (1991), no. 2, 177-189.Search in Google Scholar

STRAUCH, O.: Unsolved problems Tatra Mt. Math. Publ. 56 (2013), 109-229, DOI: 10.2478/tmmp-2013-0029. https://math.boku.ac.at/udt/unsolvedproblems.pdf10.2478/tmmp-2013-0029Search in Google Scholar

WEYL, H.: Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1916), 313-352.10.1007/BF01475864Search in Google Scholar