{"status":"public","abstract":[{"lang":"eng","text":"We introduce a new potential-theoretic definition of the dimension spectrum  of a probability measure for q > 1 and explain its relation to prior definitions. We apply this definition to prove that if  and  is a Borel probability measure with compact support in , then under almost every linear transformation from  to , the q-dimension of the image of  is ; in particular, the q-dimension of  is preserved provided . We also present results on the preservation of information dimension  and pointwise dimension. Finally, for  and q > 2 we give examples for which  is not preserved by any linear transformation into . All results for typical linear transformations are also proved for typical (in the sense of prevalence) continuously differentiable functions."}],"_id":"8527","keyword":["Mathematical Physics","General Physics and Astronomy","Applied Mathematics","Statistical and Nonlinear Physics"],"day":"19","page":"1031-1046","type":"journal_article","extern":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"IOP Publishing","author":[{"last_name":"Hunt","full_name":"Hunt, Brian R","first_name":"Brian R"},{"full_name":"Kaloshin, Vadim","last_name":"Kaloshin","first_name":"Vadim","orcid":"0000-0002-6051-2628","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"}],"publication":"Nonlinearity","intvolume":"        10","date_updated":"2021-01-12T08:19:53Z","date_created":"2020-09-18T10:50:41Z","language":[{"iso":"eng"}],"issue":"5","publication_identifier":{"issn":["0951-7715","1361-6544"]},"year":"1997","volume":10,"title":"How projections affect the dimension spectrum of fractal measures","oa_version":"None","quality_controlled":"1","article_type":"original","month":"06","article_processing_charge":"No","doi":"10.1088/0951-7715/10/5/002","citation":{"mla":"Hunt, Brian R., and Vadim Kaloshin. “How Projections Affect the Dimension Spectrum of Fractal Measures.” <i>Nonlinearity</i>, vol. 10, no. 5, IOP Publishing, 1997, pp. 1031–46, doi:<a href=\"https://doi.org/10.1088/0951-7715/10/5/002\">10.1088/0951-7715/10/5/002</a>.","short":"B.R. Hunt, V. Kaloshin, Nonlinearity 10 (1997) 1031–1046.","ista":"Hunt BR, Kaloshin V. 1997. How projections affect the dimension spectrum of fractal measures. Nonlinearity. 10(5), 1031–1046.","ama":"Hunt BR, Kaloshin V. How projections affect the dimension spectrum of fractal measures. <i>Nonlinearity</i>. 1997;10(5):1031-1046. doi:<a href=\"https://doi.org/10.1088/0951-7715/10/5/002\">10.1088/0951-7715/10/5/002</a>","ieee":"B. R. Hunt and V. Kaloshin, “How projections affect the dimension spectrum of fractal measures,” <i>Nonlinearity</i>, vol. 10, no. 5. IOP Publishing, pp. 1031–1046, 1997.","chicago":"Hunt, Brian R, and Vadim Kaloshin. “How Projections Affect the Dimension Spectrum of Fractal Measures.” <i>Nonlinearity</i>. IOP Publishing, 1997. <a href=\"https://doi.org/10.1088/0951-7715/10/5/002\">https://doi.org/10.1088/0951-7715/10/5/002</a>.","apa":"Hunt, B. R., &#38; Kaloshin, V. (1997). How projections affect the dimension spectrum of fractal measures. <i>Nonlinearity</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/0951-7715/10/5/002\">https://doi.org/10.1088/0951-7715/10/5/002</a>"},"date_published":"1997-06-19T00:00:00Z","publication_status":"published"}