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Sequences of Functions: Different Notions of Convergence and How They Are Related
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
2018 (English)Independent thesis Basic level (degree of Bachelor), 10,5 credits / 16 HE creditsStudent thesis
Abstract [en]

In this thesis we examine different types of convergence for sequences of functions and how these are related. The functions considered are real valued Lebesgue measurablefunctions defined on a subset of R. We also devote a chapter to explore when continuity of a sequence of functions is preserved under pointwise convergence, and see that this happens precisely when the convergence is quasi uniform.

Abstract [sv]

I denna uppsats utforskar vi olika typer av konvergens för funktionsföljder för att se hur de är besläktade. Funktionerna i fråga är reellvärda Lebesguemätbara funktioner definierade på delmängder av R. Vi ägnar också ett kapitel åt att undersöka när kontinuitet hos en följd av funktioner bevaras under punktvis konvergens och ser att detta händer precis då konvergensen är kvasilikformig.

Place, publisher, year, edition, pages
2018. , p. 73
Keywords [en]
Sequences of functions, convergence, quasi uniform convergence, Lp-spaces
Keywords [sv]
Funktionsföljder, konvergens, kvasilikformig konvergens, Lp-rum
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-148418ISRN: LiTH-MAT-EX--2018/06--SEOAI: oai:DiVA.org:liu-148418DiVA, id: diva2:1218166
Subject / course
Mathematics
Supervisors
Examiners
Available from: 2018-06-14 Created: 2018-06-14 Last updated: 2018-06-14Bibliographically approved

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Sätterqvist, Erik
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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf