Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 2001. Sectio Mathematicae (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 28)

LÁSZLÓ , B . & T. TÓTH, J., On very porosity and spaces of generalized uniformly distributed sequences

On very porosity and spaces of generalized uniformly distributed sequences 59 thus z <£ F*(f, 2 H- [ —

I , r). Then j(x,ó,F*(f, 2+ [g] ,r)

) > [(2+7)11+

1 > /-1 l /-1 (2 + e)/+l p[x,F*[f, 2 + r > 2 + e and letting e —» Ü we obtain the required inequality. Remark. Since the set F*(f, 2 + [p] , r) is closed in s, for each x £ s\F* (/,2+ [f] ,r) holds P x, F /,2 + r = 1. Corollary 1. Let f : R —»• R be a function. Then the set U(f

) is uniformly cr-very porous in (s, d). Corollary 2. The set S^ is uniformly a -very porous in (s, d) for every h positive integers. Proof. It follows from the fact that the function f(x) = x, x £ R. References [1] KUIPERS - NIEDERREITER

, H., Uniform distribution of sequences, Wiley, New York, (1974). [2] LÁSZLÓ, V. - .S'ALÁT, T., Uniformly distributed sequences of positive integers in Baire's space, Math. Slovaca 41. no 3 (1991), 277 - 281. [3] LÁSZLÓ, V. - ,S'ALÁT, T., The structure of some sequences spaces, and uniform distribution (mod 1), Periodica Math. Hung., Vol. 10(1) (1979), 89 - 98. [4] NIVEN, I., Uniform distribution of sequences of integers, Trans. Amer. Math. Soc

., 98 (1961), 52 - 61. [5] TKADLEC, J., Construction of some non-cr-porous sets of real line, Real Anal. Exch., 9 (1983 - 84), 473 - 482. [6] ZAJÍ

c

EK

, L., Sets of cr-porosity and sets of <r-porosity (q

), Cas. pest, mat., 101 (1976), 350 - 359.