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Search: All articles in the CMB digital archive with keyword measure-category duality

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1. CMB 2010 (vol 54 pp. 12)

Bingham, N. H.; Ostaszewski, A. J.
Homotopy and the Kestelman-Borwein-Ditor Theorem
The Kestelman--Borwein--Ditor Theorem, on embedding a null sequence by translation in (measure/category) ``large'' sets has two generalizations. Miller replaces the translated sequence by a ``sequence homotopic to the identity''. The authors, in a previous paper, replace points by functions: a uniform functional null sequence replaces the null sequence, and translation receives a functional form. We give a unified approach to results of this kind. In particular, we show that (i) Miller's homotopy version follows from the functional version, and (ii) the pointwise instance of the functional version follows from Miller's homotopy version.

Keywords:measure, category, measure-category duality, differentiable homotopy

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