Effective Capacity and Randomness of Closed Sets

Details Effective Capacity and Randomness of Closed Sets Effective Capacity and Randomness of Closed Sets

2010-06-02

arxiv.org/abs/1006.0397v1

EPTCS 24, 2010, pp. 67-76

Computer Science

Logic in Computer Science

Scientific paper

10.4204/EPTCS.24.11

We investigate the connection between measure and capacity for the space of nonempty closed subsets of {0,1}*. For any computable measure, a computable capacity T may be defined by letting T(Q) be the measure of the family of closed sets which have nonempty intersection with Q. We prove an effective version of Choquet's capacity theorem by showing that every computable capacity may be obtained from a computable measure in this way. We establish conditions that characterize when the capacity of a random closed set equals zero or is >0. We construct for certain measures an effectively closed set with positive capacity and with Lebesgue measure zero.

Affiliated with

Also associated with

No associations

Rating

Effective Capacity and Randomness of Closed Sets does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Effective Capacity and Randomness of Closed Sets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Effective Capacity and Randomness of Closed Sets will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-512919