### On the Hausdorff dimension of average type sums of Rademacher functions.

Antonis Bisbas
Source: Real Anal. Exchange Volume 29, Number 1 (2003), 139-147.

#### Abstract

We prove that for any $a, c \in (0,1)$ and any $b,d \in {\mathbb R},$ the Hausdorff dimension of $\{ x\in [0,1] : n^{-a} \sum_{j=1}^{n}r_j(x) \to b \hbox{ and } n^{-c} \sum_{j=1}^{n} r_j(x) r_{j+1}(x)\to d\},$ is equal to 1, where $\{r_n(x)\}_{n \geq 1},$ are the Rademacher functions. We give also an extension of this result.

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Primary Subjects: 28A78
Full-text: Open access