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Porosity and Approximate Derivatives

Published online by Cambridge University Press:  20 November 2018

A. M. Bruckner ,
M. Laczkovich ,
G. Petruska  and
B. S. Thomson
A. M. Bruckner
Affiliation:
University of California, Santa Barbara, California
M. Laczkovich
Affiliation:
Eötvös Lorand University, Budapest, Hungary
G. Petruska
Affiliation:
Simon Fraser University, Vancouver, British Columbia
B. S. Thomson
Affiliation:
Simon Fraser University, Vancouver, British Columbia
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In recent years, a considerable amount of research has been devoted to questions involving set porosity, particularly as it relates to differentiation theory. We may express the type of question in which we are interested by using the language of path derivatives and sequential derivatives. A path derivative of a function/is defined by writing

where at each point x a set Ex is given. A special case of the path derivative is the sequential derivative, defined by writing

where hn is a fixed sequence of nonzero numbers converging to zero.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 5 , 01 October 1986 , pp. 1149 - 1180
Copyright
Copyright © Canadian Mathematical Society 1986

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