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* [[σ-άλγεβρα]]
 
 
== Βιβλιογραφία ==
 
* {{cite book
| last = Bartle
| first = Robert G.
| title = The elements of integration and Lebesgue measure
| series = Wiley Classics Library
| publisher = John Wiley & Sons Inc.
| location = New York
| year = 1995
| pages = xii+179
| isbn = 0-471-04222-6
| nopp = true
| mr = 1312157}}
 
* {{cite book
| last = Bauer
| first = Heinz
| title = Measure and Integration Theory
| series = De Gruyter Studies in Mathematics 26
| publisher = De Gruyter
| location = Berlin
| year = 2001
| pages = 236
| isbn = 978-3-11-016719-1
| nopp = true}}
 
* {{cite book
| last = Bourbaki
| first = Nicolas
| authorlink = Nicolas Bourbaki
| title = Integration. I. Chapters 1–6. Translated from the 1959, 1965 and 1967 French originals by Sterling K. Berberian
| series = Elements of Mathematics (Berlin)
| publisher= Springer-Verlag
| location = Berlin
| year = 2004
| pages = xvi+472
| isbn = 3-540-41129-1
| nopp = true
| mr = 2018901}}
 
* {{cite book
| last = Dudley
| first = Richard M.
| title = Real analysis and probability
| series = The Wadsworth & Brooks/Cole Mathematics Series
| publisher = Wadsworth & Brooks/Cole Advanced Books & Software
| location = Pacific Grove, CA
| year = 1989
| pages = xii+436
| isbn = 0-534-10050-3
| nopp = true
| mr = 982264}} Very thorough treatment, particularly for probabilists with good notes and historical references.
 
* {{cite book
| last = Folland
| first = Gerald B.
| title = Real analysis: Modern techniques and their applications
| series = Pure and Applied Mathematics (New York)
| edition = Second
| publisher = John Wiley & Sons Inc.
| location = New York
| year = 1999
| pages = xvi+386
| isbn = 0-471-31716-0
| nopp = true
| mr = 1681462}}
 
* {{cite book
| last = Halmos
| first = Paul R.
| authorlink = Paul Halmos
| title = Measure Theory
| publisher = D. Van Nostrand Company, Inc.
| location = New York, N. Y.
| year = 1950
| pages = xi+304
| mr = 0033869}} A classic, though somewhat dated presentation.
 
* {{springer|title=Lebesgue integral|id=p/l057860}}
 
* {{Cite journal
| last = Lebesgue
| first = Henri
| authorlink = Henri Lebesgue
| title = Leçons sur l'intégration et la recherche des fonctions primitives
| publisher = Gauthier-Villars
| year = 1904
| publication-place = Paris
| postscript = <!--None-->}}
 
* {{cite book
| last = Lebesgue
| first = Henri
| authorlink = Henri Lebesgue
| title = Oeuvres scientifiques (en cinq volumes)
| publisher = Institut de Mathématiques de l'Université de Genève
| location = Geneva
| year = 1972
| pages = 405
| language = French
| mr = 0389523}}
 
*{{cite book|last1=Lieb|first1=Elliott|authorlink1=Elliott H. Lieb|last2=Loss|first2=Michael|author2-link=Michael Loss|title=Analysis|year=2001|edition=2nd|publisher=[[American Mathematical Society]]|series=Graduate Studies in Mathematics|volume=14|isbn=978-0821827833}}
 
* {{cite book
| last = Loomis
| first = Lynn H.
| title = An introduction to abstract harmonic analysis
| publisher = D. Van Nostrand Company, Inc.
| location = Toronto-New York-London
| year = 1953
| pages = x+190
| mr = 0054173}} Includes a presentation of the Daniell integral.
 
* {{cite book
| last = Munroe
| first = M. E.
| title = Introduction to measure and integration
| publisher = Addison-Wesley Publishing Company Inc.
| location = Cambridge, Mass.
| year = 1953
| pages = x+310
| mr = 0053186}} Good treatment of the theory of outer measures.
 
* {{cite book
| last = Royden
| first = H. L.
| title = Real analysis
| edition = Third
| publisher = Macmillan Publishing Company
| location = New York
| year = 1988
| pages = xx+444
| isbn = 0-02-404151-3
| mr = 1013117}}
 
* {{cite book
| last = Rudin
| first = Walter
| authorlink = Walter Rudin
| title = Principles of mathematical analysis
| edition = Third
| series = International Series in Pure and Applied Mathematics
| publisher = McGraw-Hill Book Co.
| location = New York
| year = 1976
| pages = x+342
| mr = 0385023}} Known as ''Little Rudin'', contains the basics of the Lebesgue theory, but does not treat material such as [[Fubini's theorem]].
 
* {{cite book
| last = Rudin
| first = Walter
| title = Real and complex analysis
| publisher = McGraw-Hill Book Co.
| location = New York
| year = 1966
| pages = xi+412
| mr = 0210528}} Known as ''Big Rudin''. A complete and careful presentation of the theory. Good presentation of the Riesz extension theorems. However, there is a minor flaw (in the first edition) in the proof of one of the extension theorems, the discovery of which constitutes exercise 21 of Chapter 2.
*{{Cite journal
| last = Saks
| first = Stanisław
| author-link = Stanislaw Saks
| title = Theory of the Integral
| place = [[Warszawa]]-[[Lwów]]
| publisher = G.E. Stechert & Co.
| year = 1937
| series = [http://matwbn.icm.edu.pl/ksspis.php?wyd=10&jez=pl Monografie Matematyczne]
| volume = 7
| edition = 2nd
| pages = VI+347
| url = http://matwbn.icm.edu.pl/kstresc.php?tom=7&wyd=10&jez=pl
| jfm = 63.0183.05 | zbl = 0017.30004
| postscript = <!--None-->}}. English translation by [[Laurence Chisholm Young]], with two additional notes by [[Stefan Banach]].
 
* {{cite book
| last = Shilov
| first = G. E.
| last2 = Gurevich
| first2 = B. L.
| title = Integral, measure and derivative: a unified approach. Translated from the Russian and edited by Richard A. Silverman
| series = Dover Books on Advanced Mathematics
| publisher = Dover Publications Inc.
| location = New York
| year = 1977
| pages = xiv+233
| isbn = 0-486-63519-8
| nopp = true
| mr = 0466463}} Emphasizes the [[Daniell integral]].
 
* {{citation|last=Siegmund-Schultze|first=Reinhard|chapter=Henri Lebesgue|title=Princeton Companion to Mathematics|editors=Timothy Gowers, June Barrow-Green, Imre Leader|year=2008|publisher=Princeton University Press}}.
 
* {{cite book
| last = Teschl
| first = Gerald
| authorlink = Gerald Teschl
| title = Topics in Real and Functional Analysis
| publisher = (lecture notes)
| url = http://www.mat.univie.ac.at/~gerald/ftp/book-fa/index.html}}
 
*{{cite book
| last = Yeh
| first = James
| title = Real Analysis: Theory of Measure and Integral 2nd. Edition Paperback
| publisher = World Scientific Publishing Company Pte. Ltd.
| location = Singapore
| year =2006
| pages = 760
| isbn = 978-981-256-6}}
 
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