Modes of Convergence

Rinaldo B. Schinazi
Additional contact information
Rinaldo B. Schinazi: University of Colorado, Department of Mathematics

Chapter Chapter 15 in From Classical to Modern Analysis, 2018, pp 243-266 from Springer

Abstract: Abstract Let ( X , ℳ , μ ) $$(X,\mathcal {M},\mu )$$ be a measure space. Consider L 1(μ) the space of integrable functions and let d ( f , g ) = ∫ | f − g | d μ . $$\displaystyle d(f,g)=\int |f-g|d\mu . $$ For all f, g, and h in L 1(μ) it is easy to check that d(f, g) ≥ 0, d(f, g) = d(g, f), and d ( f , g ) ≤ d ( f , h ) + d ( h , g ) . $$\displaystyle d(f,g)\leq d(f,h)+d(h,g). $$

Date: 2018
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-94583-5_15

Ordering information: This item can be ordered from
http://www.springer.com/9783319945835

DOI: 10.1007/978-3-319-94583-5_15

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().