Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach spaces

2025/02/10 by Helfter, Mathieu · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Probability (math.PR)

paper · doi:10.48550/arxiv.2502.09643

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.

Cited by

• Infinite Dimensional Multifractal Analysis of the Wiener measure

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