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.
Citation
Antonis Bisbas. "On the Hausdorff dimension of average type sums of Rademacher functions.." Real Anal. Exchange 29 (1) 139 - 147, 2003-2004.
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