Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach spaces
Helfter M. 2025. Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach spaces. Journal of Fractal Geometry.
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Abstract
For every couple of Hausdorff functions ψ and φ verifying some mild assumptions, there exists a compact subset K of the Baire space such that the φ-Hausdorff measure and the ψ-packing measure on K are both finite and positive. Such examples are then embedded in any infinite dimensional Banach space to answer positively a question of Fan on the existence of metric spaces with arbitrary scales.
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2025-11-07
Journal Title
Journal of Fractal Geometry
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EMS Press
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Cite this
Helfter M. Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach spaces. Journal of Fractal Geometry. 2025. doi:10.4171/jfg/177
Helfter, M. (2025). Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach spaces. Journal of Fractal Geometry. EMS Press. https://doi.org/10.4171/jfg/177
Helfter, Mathieu. “Sets with Arbitrary Hausdorff and Packing Scales in Infinite Dimensional Banach Spaces.” Journal of Fractal Geometry. EMS Press, 2025. https://doi.org/10.4171/jfg/177.
M. Helfter, “Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach spaces,” Journal of Fractal Geometry. EMS Press, 2025.
Helfter M. 2025. Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach spaces. Journal of Fractal Geometry.
Helfter, Mathieu. “Sets with Arbitrary Hausdorff and Packing Scales in Infinite Dimensional Banach Spaces.” Journal of Fractal Geometry, EMS Press, 2025, doi:10.4171/jfg/177.
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