[{"title":"Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach spaces","month":"11","article_type":"original","scopus_import":"1","day":"07","DOAJ_listed":"1","doi":"10.4171/jfg/177","year":"2025","author":[{"id":"7d296fbe-e2c6-11ee-84d3-d5c2945f9a57","full_name":"Helfter, Mathieu","last_name":"Helfter","first_name":"Mathieu"}],"status":"public","quality_controlled":"1","corr_author":"1","type":"journal_article","oa":1,"date_created":"2025-12-19T10:15:37Z","main_file_link":[{"url":"https://doi.org/10.4171/jfg/177","open_access":"1"}],"abstract":[{"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.","lang":"eng"}],"_id":"20839","article_processing_charge":"Yes","date_updated":"2026-02-16T11:44:20Z","OA_place":"publisher","OA_type":"gold","language":[{"iso":"eng"}],"department":[{"_id":"VaKa"}],"publication_identifier":{"issn":["2308-1309"],"eissn":["2308-1317"]},"citation":{"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.","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>","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).","ista":"Helfter M. 2025. Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach spaces. Journal of Fractal Geometry.","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>"},"date_published":"2025-11-07T00:00:00Z","oa_version":"Published Version","publisher":"EMS Press","publication_status":"epub_ahead","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Journal of Fractal Geometry"}]