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Convergence of Functions

In: Essentials of Measure Theory

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  • Carlos S. Kubrusly

    (Catholic University of Rio de Janeiro, Electrical Engineering Department)

Abstract

Major convergence concepts for sequences of real-valued functions will be considered in this chapter. We have already met four convergence concepts so far (viz., pointwise, uniform, almost everywhere, and convergence in L p ). These are reviewed and compared in this section. Further concepts, namely, convergence in measure, uniform almost everywhere, and almost uniform convergence, will be discussed and compared in subsequent sections.

Suggested Citation

  • Carlos S. Kubrusly, 2015. "Convergence of Functions," Springer Books, in: Essentials of Measure Theory, edition 1, chapter 6, pages 89-107, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-22506-7_6
    DOI: 10.1007/978-3-319-22506-7_6
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