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2013/2014 The Denjoy-Young-Saks Theorem in Higher Dimensions: A Survey
Ákos K. Matszangosz
Real Anal. Exchange 40(1): 1-36 (2013/2014).


The classical theorem of Denjoy, Young and Saks gives a relation between Dini derivatives of a real variable function that holds almost everywhere. We present what is known in the one and two variable case with an emphasis on the latter. Relations that hold a.e. in both the measure and category sense are considered. Classical and approximate derivatives are both discussed.


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Ákos K. Matszangosz. "The Denjoy-Young-Saks Theorem in Higher Dimensions: A Survey." Real Anal. Exchange 40 (1) 1 - 36, 2013/2014.


Published: 2013/2014
First available in Project Euclid: 1 July 2015

zbMATH: 06848821
MathSciNet: MR3365388

Primary: 26B05
Secondary: 26A24 , 26A27

Keywords: a.e. differentability , approximate derivatives , Denjoy-Young-Saks theorem , Dini derivates , directed derivatives , directional derivatives , two variable functions

Rights: Copyright © 2015 Michigan State University Press

Vol.40 • No. 1 • 2013/2014
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