Extension of Functions with Small Oscillation
| dc.creator | Leung, Denny H. | |
| dc.creator | Tang, Wee-Kee | |
| dc.date | 2005-05-10 | |
| dc.date.accessioned | 2026-07-07T05:19:45Z | |
| dc.date.available | 2026-07-07T05:19:45Z | |
| dc.description | A classical theorem of Kuratowski says that every Baire one function on a G_δsubspace of a Polish (= separable completely metrizable) space X can be extended to a Baire one function on X. Kechris and Louveau introduced a finer gradation of Baire one functions into small Baire classes. A Baire one function f is assigned into a class in this heirarchy depending on its oscillation index β(f). We prove a refinement of Kuratowski's theorem: if Y is a subspace of a metric space X and f is a real-valued function on Y such that β_{Y}(f)<ω^α, α< ω_1, then f has an extension F onto X so that β_X(F)is not more than ω^α. We also show that if f is a continuous real valued function on Y, then f has an extension F onto X so that β_{X}(F)is not more than 3. An example is constructed to show that this result is optimal. | |
| dc.identifier | https://arxiv.org/abs/math/0505168 | |
| dc.identifier | http://arxiv.org/abs/math/0505168 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75132 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Functional Analysis | |
| dc.subject | 26A21; 03E15, 54C30 | |
| dc.title | Extension of Functions with Small Oscillation | |
| dc.type | text |