The Stepanov theorem for Q-valued functions

In this work we prove the Stepanov differentiation theorem for multiple-valued functions. This theorem is proved in the wide generality of metric-space-multiple-valued functions without relying on a Lipschitz extension result. General definitions of differentiability and approximate differentiabilit...

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Bibliographic Details
Published in:arXiv.org 2024-02
Main Author: De Donato, Paolo
Format: Article
Language:English
Subjects:
Metric space
Theorems
Online Access:Get full text
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Summary:In this work we prove the Stepanov differentiation theorem for multiple-valued functions. This theorem is proved in the wide generality of metric-space-multiple-valued functions without relying on a Lipschitz extension result. General definitions of differentiability and approximate differentiability for functions between suitable metric spaces are also introduced.
ISSN:2331-8422