ABSTRACT
This paper investigates the extension of magnitude continuity results to ℓN p spaces for p≠1, developing a framework for analyzing magnitude continuity via weight measures and generalized thickenings, and discussing the unique challenges posed by the p=∞ case.
PAPER · PDF
Loading PDF…
Key findings
Establishes that for p∈(1,∞), the unit ball of ℓN p has strictly positive magnitude.
Develops a framework for analyzing magnitude continuity via weight measures and generalized thickenings.
Characterizes skew finite subsets in ℓN p for general p.
Provides explicit formulas for weight measures of p-ball thickenings.
Discusses the unique challenges posed by the p=∞ case.
Limitations & open questions
Analysis of the failure of the standard approach for p >2 and proposed modifications are discussed but not fully resolved.