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