On a Problem of Zygmund

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Abstract

It is proved that there exists an integrable function on [0, 1]2 whose integral is nondifferentiable in each direction belonging to a set everywhere dense in [0, 2π] but is strongly differentiable.
Original languageAmerican English
JournalMathematical Notes
Volume64
DOIs
StatePublished - Nov 1998

Disciplines

  • Mathematics

Keywords

  • Integrable Function
  • Strong Differentiability
  • Zygmund Problem
  • the Jessen-marcinkiewicz-zygmund Theorem

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