Publ. Math. Debrecen 58 / 4 (2001), 751–778 Distribution functions of ratio sequences By OTO STRAUCH (Bratislava) and J ´ ANOS T. T ´ OTH (Ostrava) Dedicated to Prof. K´alm´ an Gy˝ory on his 60th birthday Abstract. The paper deals with a block sequence defined by X n = x 1 x n , x 2 x n ,..., x n x n where x n is an increasing sequence of positive integers. We discuss the set of all distri- bution functions of such sequences. 1. Introduction For every n =1, 2,... , let X n =(x n,1 ,...,x n,N n ) be a finite sequence in [0, 1]. The infinite sequence ω =(x 1,1 ,...,x 1,N 1 ,x 2,1 ,...,x 2,N 2 ... ), abbreviated as ω =(X n ) ∞ n=1 , will be called a block sequence associated with the sequence of single blocks X n , n =1, 2,... . We will distinguish Mathematics Subject Classification : 11K31. Key words and phrases : block sequences, ratio sequences, distribution functions, asym- ptotic density. This research was supported by the Slovak Academy of Sciences Grant 5123 and the GAAV A 1187 101.