Scaling properties of Hausdorff and packing measures
Copyright policy )Scaling properties of Hausdorff and packing measures
Let \(\theta \) be a continuous increasing function defined on the nonnegative number line with some restriction. Among other results, the authors characterize those function \(\theta \) such that the corresponding Hausdorff or packing measure with gauge function \(\theta \) scales with exponent \(\alpha \) by showing it must be a product of a power function with exponent \(\alpha \) and a slowly varying function.
- University College London United Kingdom
- University of North Texas United States
- University of North Texas System United States
Fractals, Hausdorff and packing measures, slowly varying function, packing measure, scaling, power function, gauge function, Rate of growth of functions, orders of infinity, slowly varying functions, Hausdorff measure
Fractals, Hausdorff and packing measures, slowly varying function, packing measure, scaling, power function, gauge function, Rate of growth of functions, orders of infinity, slowly varying functions, Hausdorff measure
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