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Porosity and Approximate Derivatives

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.