A martingale proof of the theorem by Jessen, Marcinkiewicz and Zygmund on strong differentiation of integrals

Malgorsata Kuchta; Michal Morayne; Slawomir Solecki

Séminaire de probabilités de Strasbourg (2001)

  • Volume: 35, page 158-161

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Kuchta, Malgorsata, Morayne, Michal, and Solecki, Slawomir. "A martingale proof of the theorem by Jessen, Marcinkiewicz and Zygmund on strong differentiation of integrals." Séminaire de probabilités de Strasbourg 35 (2001): 158-161. <http://eudml.org/doc/114057>.

@article{Kuchta2001,
author = {Kuchta, Malgorsata, Morayne, Michal, Solecki, Slawomir},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {differentiation of integrals; strong Lebesgue point; convergence of multi-indexed martingales},
language = {eng},
pages = {158-161},
publisher = {Springer - Lecture Notes in Mathematics},
title = {A martingale proof of the theorem by Jessen, Marcinkiewicz and Zygmund on strong differentiation of integrals},
url = {http://eudml.org/doc/114057},
volume = {35},
year = {2001},
}

TY - JOUR
AU - Kuchta, Malgorsata
AU - Morayne, Michal
AU - Solecki, Slawomir
TI - A martingale proof of the theorem by Jessen, Marcinkiewicz and Zygmund on strong differentiation of integrals
JO - Séminaire de probabilités de Strasbourg
PY - 2001
PB - Springer - Lecture Notes in Mathematics
VL - 35
SP - 158
EP - 161
LA - eng
KW - differentiation of integrals; strong Lebesgue point; convergence of multi-indexed martingales
UR - http://eudml.org/doc/114057
ER -

References

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  1. [C] R. Cairoli, Une inégalité pour martingales à indices multiples et ses applications, Séminaire de Probabilités IV, Lecture Notes in Mathematics124, 1970, Springer-Verlag, Berlin, 1-27. Zbl0218.60045MR270424
  2. [Ch] S.D. Chatterji, Les martingales et leurs applications analytiques, École d'Été de Probabilités, Processus Stochastiques, Lecture Notes in Mathematics307, 1973, Springer-Verlag, Berlin, 27-146. MR448536
  3. [DM] C. Dellacherie and P.-A. Meyer, Probabilités et Potentiel, Hermann, Paris, 1980. MR566768
  4. [JMZ] B. Jessen, J. Marcinkiewicz and A. Zygmund, Note on the differentiability of multiple integrals, Fundamenta Mathematicae25, 1935, 217-234. Zbl0012.05901JFM61.0255.01
  5. [M] B. Maisonneuve, Surmartingales-mesures, Séminaire de Probabilités XV, Lecture Notes in Mathematics850, 1981, Springer-Verlag, Berlin, 347-350. Zbl0461.60063MR622575
  6. [MS] M. Morayne and S. Solecki, Martingale proof of the existence of Lebesgue points, Real Analysis Exchange15, 1989-90, 401-406. Zbl0701.26009MR1042558

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