Pointwise dimensions of general Moran measures with open set condition. (English) Zbl 1219.28010
Summary: Recently, Lou and Wu obtained the formulas of pointwise dimensions of some Moran measures on Moran sets in \(\mathbb R^{d}\) under the strong separation condition [M. Lou and M. Wu, Sci. China, Math. 53, No. 5, 1283–1292 (2010; Zbl 1200.28011)]. We prove that the result is still true under the open set condition. Due to the lack of the strong separation condition, our approach is essentially different from that used by Lou and Wu. We also obtain the formulas of the Hausdorff and packing dimensions of the Moran measures and discuss some interesting examples.
Citations:
Zbl 1200.28011References:
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