Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4615677 | Journal of Mathematical Analysis and Applications | 2015 | 8 Pages |
Abstract
We consider the Banach space consisting of real-valued continuous functions on an arbitrary compact metric space. It is known that for a prevalent (in the sense of Hunt, Sauer and Yorke) set of functions the Hausdorff dimension of the image is as large as possible, namely 1. We extend this result by showing that 'prevalent' can be replaced by '1-prevalent', i.e. it is possible to witness this prevalence using a measure supported on a one dimensional subspace. Such one dimensional measures are called probes and their existence indicates that the structure and nature of the prevalence is simpler than if a more complicated 'infinite dimensional' witnessing measure has to be used.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Jonathan M. Fraser, James T. Hyde,