Abstract
We give a martingale proof of the theorem by Jessen, Marcinkiewicz and Zygmund on almost everywhere strong differentiability of functions on \({\bf {R}}^n\) belonging to \(\rm {L(Log + L)^{n-1}}\). The proof is based on Cairoli’s theorem on convergence of multi-indexed martingales.
Mathematics Subject Classification (2000):
- 60GXX
- 60HXX
- 60JXX
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© 2001 Springer-Verlag Berlin/Heidelberg
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Kuchta, M., Morayne, M., Solecki, S. (2001). A Martingale Proof of the Theorem by Jessen, Marcinkiewicz and Zygmund on Strong Differentiation of Integrals. In: Azéma, J., Émery, M., Ledoux, M., Yor, M. (eds) Séminaire de Probabilités XXXV. Lecture Notes in Mathematics, vol 1755. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44671-2_11
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DOI: https://doi.org/10.1007/978-3-540-44671-2_11
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41659-3
Online ISBN: 978-3-540-44671-2
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