An extension of a theorem of Banach
type: Item
instance of: scholarly article
title: An extension of a theorem of Banach
zbMATH Open document ID: 0863.26011
DOI: 10.1007/BF01195237
author: Pier Mario Gandini
published in: Archiv der Mathematik
publication date: 1997-06-03T00:00:00Z
review text: The main result of the paper says that for nearly all functions which are continuous on the \(n\)-dimensional cube at each point \(P\) of the interior of the cube and for each direction upper and lower directional derivatives are \(+\infty\) and \(-\infty\), respectively. Here ``nearly all'' means except a sigma porous set.
reviewed by: Władysław Wilczyński
Mathematics Subject Classification ID: 26B05
Mathematics Subject Classification ID: 26B35
zbMATH DE Number: 938597
zbMATH Keywords: directional derivatives
zbMATH Keywords: sigma porous set
MaRDI profile type: Publication
cites work: Über die Baire'sche Kategorie gewisser Funktionenmengen
cites work: Differentiation of real functions
cites work: Porosity and typical properties of real-valued continuous functions
cites work: Sets of $\sigma$-porosity and sets of $\sigma $-porosity $(q)$
full work available at URL: https://doi.org/10.1007/bf01195237
OpenAlex ID: W1995750743
description: scientific article; zbMATH DE number 938597