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Residually many BV homeomorphisms map a null set onto a set of full measure
Published online by Cambridge University Press: 27 December 2018
Abstract
Let Q be the open unit square in ℝ2. We prove that in a natural complete metric space of BV homeomorphisms f : Q → Q with f|∂Q = Id, residually many homeomorphisms (in the sense of Baire categories) map a null set onto a set of full measure, and vice versa. Moreover, we observe that for 1 ⩽ p < 2, the family of W1,p homemomorphisms satisfying the above property is of the first category.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 4 , August 2019 , pp. 1047 - 1059
- Copyright
- Copyright © Royal Society of Edinburgh 2018
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