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We prove a direct conversion of a constructive martingale into a measure of impossibility and vice versa such that their success sets, for a suitably defined class of computable probability measures, are equal. The direct conversion is then generalized to give a new characterization of constructive dimensions, in particular, the constructive Hausdorff dimension, the constructive packing dimension, and their generalizations, the constructive scaled dimension and the constructive scaled strong dimension (\u00a9 2009 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200710087","type":"journal-article","created":{"date-parts":[[2009,1,20]],"date-time":"2009-01-20T07:18:21Z","timestamp":1232435901000},"page":"185-200","source":"Crossref","is-referenced-by-count":1,"title":["A characterization of constructive dimension"],"prefix":"10.1002","volume":"55","author":[{"given":"Satyadev","family":"Nandakumar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2009,1,20]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","unstructured":"K. B.Athreya J. M.Hitchcock J. H.Lutz andE.Mayordomo Effective strong dimension algorithmic information and computational complexity. 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