## The Dimensions of Individual Strings and Sequences (2003)

by
Jack H. Lutz

Venue: | INFORMATION AND COMPUTATION |

Citations: | 93 - 10 self |

### BibTeX

@ARTICLE{Lutz03thedimensions,

author = {Jack H. Lutz},

title = {The Dimensions of Individual Strings and Sequences},

journal = {INFORMATION AND COMPUTATION},

year = {2003},

volume = {187},

pages = {2003}

}

### Years of Citing Articles

### OpenURL

### Abstract

A constructive version of Hausdorff dimension is developed using constructive supergales, which are betting strategies that generalize the constructive supermartingales used in the theory of individual random sequences. This constructive dimension is used to assign every individual (infinite, binary) sequence S a dimension, which is a real number dim(S) in the interval [0, 1]. Sequences that