Abstract
AbstractIn the context of Kolmogorov's algorithmic approach to the foundations of probability, Martin‐Löf defined the concept of an individual random sequence using the concept of a constructive measure 1 set. Alternate characterizations use constructive martingales and measures of impossibility. 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 (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
