---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
_id: '20839'
abstract:
- lang: eng
  text: 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.
article_processing_charge: Yes
article_type: original
author:
- first_name: Mathieu
  full_name: Helfter, Mathieu
  id: 7d296fbe-e2c6-11ee-84d3-d5c2945f9a57
  last_name: Helfter
citation:
  ama: Helfter M. Sets with arbitrary Hausdorff and packing scales in infinite dimensional
    Banach spaces. <i>Journal of Fractal Geometry</i>. 2025. doi:<a href="https://doi.org/10.4171/jfg/177">10.4171/jfg/177</a>
  apa: Helfter, M. (2025). Sets with arbitrary Hausdorff and packing scales in infinite
    dimensional Banach spaces. <i>Journal of Fractal Geometry</i>. EMS Press. <a href="https://doi.org/10.4171/jfg/177">https://doi.org/10.4171/jfg/177</a>
  chicago: Helfter, Mathieu. “Sets with Arbitrary Hausdorff and Packing Scales in
    Infinite Dimensional Banach Spaces.” <i>Journal of Fractal Geometry</i>. EMS Press,
    2025. <a href="https://doi.org/10.4171/jfg/177">https://doi.org/10.4171/jfg/177</a>.
  ieee: M. Helfter, “Sets with arbitrary Hausdorff and packing scales in infinite
    dimensional Banach spaces,” <i>Journal of Fractal Geometry</i>. EMS Press, 2025.
  ista: Helfter M. 2025. Sets with arbitrary Hausdorff and packing scales in infinite
    dimensional Banach spaces. Journal of Fractal Geometry.
  mla: Helfter, Mathieu. “Sets with Arbitrary Hausdorff and Packing Scales in Infinite
    Dimensional Banach Spaces.” <i>Journal of Fractal Geometry</i>, EMS Press, 2025,
    doi:<a href="https://doi.org/10.4171/jfg/177">10.4171/jfg/177</a>.
  short: M. Helfter, Journal of Fractal Geometry (2025).
corr_author: '1'
date_created: 2025-12-19T10:15:37Z
date_published: 2025-11-07T00:00:00Z
date_updated: 2026-06-18T18:26:33Z
day: '07'
ddc:
- '500'
department:
- _id: VaKa
doi: 10.4171/jfg/177
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.4171/jfg/177
month: '11'
oa: 1
oa_version: Published Version
publication: Journal of Fractal Geometry
publication_identifier:
  eissn:
  - 2308-1317
  issn:
  - 2308-1309
publication_status: epub_ahead
publisher: EMS Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach
  spaces
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...