University · Mathematics · Measure Theory and Lebesgue Integration

Convergence in Measure and Egorov's Theorem

4 Abschnitte1 Karteikarten-Decks1 Quizze

How convergence in measure compares to almost-everywhere and Lp convergence, the classic 'typewriter sequence' showing convergence in measure does not imply a.e. convergence, and Egorov's theorem (Dmitri Egorov, 1911), which shows a.e. convergence on a finite measure space becomes uniform outside a set of arbitrarily small measure.

Inhaltsübersicht

  • Modes of Convergence for Measurable Functions
  • Convergence in Measure and Its Relation to a.e. Convergence
  • Egorov's Theorem: Almost Uniform Convergence
  • The Typewriter Sequence and Other Counterexamples
Diagram of an exceptional set shrinking to measure zero as n increases
Pixabay – Pixabay License

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