𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A characterization of constructive dimension

✍ Scribed by Satyadev Nandakumar

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
173 KB
Volume
55
Category
Article
ISSN
0044-3050

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

In the context of Kolmogorov's algorithmic approach to the foundations of probability, Martin‐LΓΆf 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 (Β© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

πŸ“œ SIMILAR VOLUMES

A Characterization of Dimension Function
A Characterization of Dimension Functions of Wavelets
✍ Marcin Bownik; Ziemowit Rzeszotnik; Darrin Speegle πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 200 KB

This paper is devoted to the study of the dimension functions of (multi)wavelets, which was introduced and investigated by P. Auscher in 1995 (J. Geom. Anal. 5,. Our main result provides a characterization of functions which are dimension functions of a (multi)wavelet. As a corollary, we obtain that

Construction of Modules with Finite Homo
Construction of Modules with Finite Homological Dimensions
✍ Oana Veliche πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 163 KB

A new homological dimension, called G \* -dimension, is defined for every finitely generated module M over a local noetherian ring R. It is modeled on the CI-dimension of Avramov, Gasharov, and Peeva and has parallel properties. In particular, a ring R is Gorenstein if and only if every finitely gen

A Constructive Enumeration of Fullerenes
A Constructive Enumeration of Fullerenes
✍ Gunnar Brinkmann; Andreas W.M. Dress πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 215 KB

In this paper, a fast and complete method to enumerate fullerene structures is given. It is based on a top-down approach, and it is fast enough to generate, for example, all 1812 isomers of C in less than 20 s on an SGI-workstation. The 60 method described can easily be generalized for 3-regular sph