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On Peano and Riemann derivatives

✍ Scribed by Ivan Ginchev; Matteo Rocca

Publisher
Springer Milan
Year
2000
Tongue
Italian
Weight
95 KB
Volume
49
Category
Article
ISSN
0009-725X

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A function f : ‫ޒ‬ Βͺ ‫ޒ‬ is said to have an nth Generalized Peano Derivative Ε½ . GPD at x if f is continuous in a neighborhood of x and there exists an integer Ε½ . kG0 such that the kth primitive of f has a k q n th Peano derivative at x. An example shows that sometimes no such k exists. In this cas

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## Abstract The notion of Peano differentiability generalizes the differentiability in the usual sense to higher order. Peano differentiable functions have derivatives which are sometimes differentiable or continuous or not even locally bounded. We give a complete characterisation of the sets in wh