Abstract
In this paper, we consider decomposition of continuous functions in [Formula: see text] in terms of Hausdorff dimension and lower box dimension. Precisely, we show that, given real numbers [Formula: see text], any real-valued continuous function in [Formula: see text] can be decomposed into a sum of two real-valued continuous functions each having a graph of Hausdorff dimension [Formula: see text] and lower box dimension [Formula: see text]. This generalizes a theorem of Wingren, also Wu and the present author. We also consider the arbitrary decomposition of continuous functions in terms of Hausdorff dimension and lower box dimension.
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