Jump to content
Main menu
Main menu
move to sidebar
hide
Navigation
Main page
Recent changes
Random page
Help about MediaWiki
Special pages
Niidae Wiki
Search
Search
Appearance
Create account
Log in
Personal tools
Create account
Log in
Pages for logged out editors
learn more
Contributions
Talk
Editing
Measure (mathematics)
(section)
Page
Discussion
English
Read
Edit
View history
Tools
Tools
move to sidebar
hide
Actions
Read
Edit
View history
General
What links here
Related changes
Page information
Appearance
move to sidebar
hide
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
==Bibliography== {{refbegin}} * [[Robert G. Bartle]] (1995) ''The Elements of Integration and Lebesgue Measure'', Wiley Interscience. * {{citation | last=Bauer|first=Heinz|authorlink=Heinz Bauer|title=Measure and Integration Theory|year=2001|publisher=de Gruyter|location=Berlin|isbn=978-3110167191}} * {{citation | last=Bear|first=H.S.|title=A Primer of Lebesgue Integration|year=2001|publisher=Academic Press|location=San Diego|isbn=978-0120839711}} * {{cite book |last1=Berberian |first1=Sterling K |title=Measure and Integration |date=1965 |publisher=MacMillan}} * {{citation | last=Bogachev|first=Vladimir I.|authorlink=Vladimir Bogachev|title=Measure theory|year=2006|publisher=Springer|location=Berlin|isbn=978-3540345138}} * {{citation | last=Bourbaki| first=Nicolas | title=Integration I | year=2004 | publisher=[[Springer Verlag]] | isbn=3-540-41129-1}} Chapter III. * {{cite book |last=Dudley|first=Richard M.|authorlink=Richard M. Dudley| title=Real Analysis and Probability | year=2002 |publisher=Cambridge University Press|isbn=978-0521007542}} * {{cite book |last1=Edgar |first1=Gerald A. |title=Integral, Probability, and Fractal Measures |date=1998 |publisher=Springer |isbn=978-1-4419-3112-2}} * {{cite book |last1=Folland |first1=Gerald B. |authorlink=Gerald Folland|title=Real Analysis: Modern Techniques and Their Applications |date=1999 |publisher=Wiley |isbn=0-471-31716-0 |edition=Second}} * Federer, Herbert. Geometric measure theory. Die Grundlehren der mathematischen Wissenschaften, Band 153 Springer-Verlag New York Inc., New York 1969 xiv+676 pp. * {{cite book |last1=Fremlin |first1=D.H. |title=Measure Theory, Volume 2: Broad Foundations |date=2016 |publisher=Torres Fremlin |edition=Hardback}} Second printing. * {{cite book |last1=Hewitt |first1=Edward |last2=Stromberg |first2=Karl |title=Real and Abstract Analysis: A Modern Treatment of the Theory of Functions of a Real Variable |date=1965 |publisher=Springer |isbn=0-387-90138-8}} * {{citation | last=Jech| first=Thomas | title=Set Theory: The Third Millennium Edition, Revised and Expanded | year=2003 | publisher=[[Springer Verlag]] | isbn=3-540-44085-2}} * [[R. Duncan Luce]] and Louis Narens (1987). "measurement, theory of", ''The [[New Palgrave: A Dictionary of Economics]]'', v. 3, pp. 428β32. * {{cite journal |last1=Luther |first1=Norman Y |title=A decomposition of measures |journal=Canadian Journal of Mathematics |date=1967 |volume=20 |pages=953β959 |doi=10.4153/CJM-1968-092-0 |s2cid=124262782 |doi-access=free }} * {{cite book |last1=Mukherjea |first1=A |last2=Pothoven |first2=K |title=Real and Functional Analysis, Part A: Real Analysis |date=1985 |publisher=Plenum Press |edition=Second |url=https://link.springer.com/book/9781441974587}} ** The first edition was published with ''Part B: Functional Analysis'' as a single volume: {{cite book |last1=Mukherjea |first1=A |last2=Pothoven |first2=K |title=Real and Functional Analysis |date=1978 |publisher=Plenum Press |doi=10.1007/978-1-4684-2331-0 |isbn=978-1-4684-2333-4 |edition=First |url=https://link.springer.com/book/10.1007/978-1-4684-2331-0}} * M. E. Munroe, 1953. ''Introduction to Measure and Integration''. Addison Wesley. * {{cite book |last1=Nielsen |first1=Ole A |title=An Introduction to Integration and Measure Theory |date=1997 |publisher=Wiley |isbn=0-471-59518-7}} * {{Citation|author=K. P. S. Bhaskara Rao and M. Bhaskara Rao|title=Theory of Charges: A Study of Finitely Additive Measures| publisher=Academic Press|location=London|year=1983|pages=x + 315|isbn=0-12-095780-9}} * {{cite book |last1=Royden |first1=H.L. |last2=Fitzpatrick |first2=P.M. |author1-link=Halsey Royden |title=Real Analysis |date=2010 |publisher=Prentice Hall |page=342, Exercise 17.8 |edition=Fourth}} First printing. There is a later (2017) second printing. Though usually there is little difference between the first and subsequent printings, in this case the second printing not only deletes from page 53 the Exercises 36, 40, 41, and 42 of Chapter 2 but also offers a (slightly, but still substantially) different presentation of part (ii) of Exercise 17.8. (The second printing's presentation of part (ii) of Exercise 17.8 (on the Luther{{sfn|Luther|1967|loc=Theorem 1}} decomposition) agrees with usual presentations,{{sfn|Mukherjea|Pothoven|1985|p=90}}{{sfn|Folland|1999|p=27|loc=Exercise 1.15.a}} whereas the first printing's presentation provides a fresh perspective.) * Shilov, G. E., and Gurevich, B. L., 1978. ''Integral, Measure, and Derivative: A Unified Approach'', Richard A. Silverman, trans. Dover Publications. {{isbn|0-486-63519-8}}. Emphasizes the [[Daniell integral]]. * {{citation | last = Teschl| first = Gerald| author-link = Gerald Teschl| title = Topics in Real Analysis| url = https://www.mat.univie.ac.at/~gerald/ftp/book-ra/index.html|publisher = (lecture notes)}} * {{cite book|last1=Tao|first1=Terence|author-link=Terence Tao|title=An Introduction to Measure Theory|date=2011|publisher=American Mathematical Society|location=Providence, R.I.|isbn=9780821869192}} * {{cite book|last1=Weaver|first1=Nik|title=Measure Theory and Functional Analysis|date=2013|publisher= [[World Scientific]]|isbn=9789814508568}} {{refend}}
Summary:
Please note that all contributions to Niidae Wiki may be edited, altered, or removed by other contributors. If you do not want your writing to be edited mercilessly, then do not submit it here.
You are also promising us that you wrote this yourself, or copied it from a public domain or similar free resource (see
Encyclopedia:Copyrights
for details).
Do not submit copyrighted work without permission!
Cancel
Editing help
(opens in new window)
Search
Search
Editing
Measure (mathematics)
(section)
Add topic