Bijections and metric spaces induced by some collective properties of concave Young-functions

Simple item page
dc.creatorAgbeko, N. K.
dc.date2006-05-07
dc.date.accessioned2026-07-07T07:13:59Z
dc.date.available2026-07-07T07:13:59Z
dc.descriptionFor each ${\small b\in(0, \infty)}$ we intend to generate a decreasing sequence of subsets $(\mathcal{Y}_{b}^{(n)}) \subset Y_{\mathrm{conc}}$ depending on $b$ such that whenever $n\in\mathbb{N}$, then $\mathcal{A}\cap\mathcal{Y}_{b}^{(n)}% $ is dense in $\mathcal{Y}_{b}^{(n)}$ and the following four sets $\mathcal{Y}_{b}^{(n)}$, $\mathcal{Y}_{b}^{(n) }\backslash(\mathcal{A}\cap\mathcal{Y}_{b}^{(n)}) $, $\mathcal{A}\cap\mathcal{Y}_{b}^{(n)}$ and $\mathcal{Y}_{\mathrm{conc}}$ are pairwise equinumerous. Among others we also show that if $f$ is any measurable function on a measure space $(Ω,\mathcal{F},λ) $ and $p\in[ 1,\infty) $ is an arbitrary number then the quantities $\left\Vert f\right\Vert_{L^{p}}$ and $\sup_{Φ\in\widetilde{\mathcal{Y}_{\mathrm{conc}}}}(Φ(1)) ^{-1}\left\Vert Φ\circ| f| \right\Vert_{L^{p}}$ are equivalent, in the sense that they are both either finite or infinite at the same time.
dc.descriptionWe note that in [3], Lemma 7 is wrong. Fortunately, nothing is lost. We should like to refer the reader to the referee's note for the Mathematical Reviews: MR2148839(2006e:26005)
dc.identifierhttps://arxiv.org/abs/math/0605181
dc.identifierhttp://arxiv.org/abs/math/0605181
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112689
dc.subjectGeneral Mathematics
dc.subjectMetric Geometry
dc.subjectPrimary 26A06, 54E35, 26A42; Secondary 11J83, 28A25, 47H10
dc.titleBijections and metric spaces induced by some collective properties of concave Young-functions
dc.typetext

Files

Collections

arXiv