On the convergence of multiplicatively orthogonal series

On generalized Takagi functions

“…Introduction. Using some results by the Hungarian school [2], [3], [10], [11], [12], and [13], we get some properties of the function defined by f, (x) = ~c, ~0. This example is defined as follows: Set and give necessary and sufficient conditions in order that f is nowhere differentiable, differentiable on a set of continuum or absolutely continuous, resp.…”

Functional central limit theorem and log log law for multiplicative systems

“…In this paper we lmve the analogous theorems for a multiplicative system of random variables in the following sense: DEFINITION (Alexits [1] Here, under somewhat stronger condition, the equality sign also holds (cf. R6-v6sz [7]) which suggests that the corresponding extension of Theorem 3 is also true.…”

Probability inequalities for multiplicative sequences of random variables

“…Note that multiplicative systems were introduced by Alexits in his famous monograph [1]. It was proved by Alexits-Sharma [2] that uniformly bounded multiplicative systems are convergence systems. Recall that an infinite system of random variables {φ k } is said to be a convergence system if the condition k a 2 k < ∞ implies almost sure convergence of series k a k φ k .…”