Theorems on the smoothness of the right inverse
type: Item
instance of: scholarly article
title: Theorems on the smoothness of the right inverse
zbMATH Open document ID: 0656.26013
DOI: 10.1007/BF01138333
author: N. M. Isakov
published in: Mathematical Notes
publication date: 1987-01-01T00:00:00Z
review text: Let K be a compact subset in \(R^ n\) and let f be a Lipschitz mapping from K into \(R^ n\). Then there exists a countable family of mappings \(g\nu\) from f(K) into K (\(\nu\in N)\), approximately differentiable on f(K), such that for each \(y\in f(K)\) we have \(g_{\nu}(y)\in f^{- 1}(y)\quad (\nu \in N)\) and the set \(\{g_{\nu}(y)\}_{\nu \in N}\) is everywhere dense in \(f^{-1}(y)\). Moreover, each mapping g, measurable on f(K), such that \(f\circ g=id_{f(K)}\) satisfies the following condition. For each \(\epsilon >0\) there exists a compactum \(C\subset f(K)\) such that \(\mu C>\mu f(K)-\epsilon\) and \(g|_ C\) is Lipschitzian (\(\mu\) is the Lebesgue measure on \(R^ n)\).
Mathematics Subject Classification ID: 26B05
Mathematics Subject Classification ID: 26B10
zbMATH DE Number: 4071253
zbMATH Keywords: compact subset in \(R^ n\)
zbMATH Keywords: Lipschitz mapping
zbMATH Keywords: approximately differentiable
MaRDI profile type: Publication
cites work: Q5779004
cites work: Q5565773
cites work: Q5667133
description: scientific article; zbMATH DE number 4071253