Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Introduction Read chapter Read first chapter

2016 | OriginalPaper | Chapter

4. Measures

Authors : H. G. Dales, F. K. Dashiell Jr., A. T.-M. Lau, D. Strauss

Published in: Banach Spaces of Continuous Functions as Dual Spaces

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this chapter, we shall study the (complex) Banach lattice M(K) consisting of all complex-valued, regular Borel measures on a locally compact space K and, in particular, the positive measures in M(K), which form the cone M(K)+. The Banach space M(K) is isometrically isomorphic to the dual of C  0(K). In \(\S\)4.2, we shall discuss the linear spaces of discrete measures and of continuous measures on K.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Banach Algebras and C ∗-Algebras
next chapter Hyper-Stonean Spaces
Literature
2.
3.
F. Albiac, N. J. Kalton, Topics in Banach Space Theory. Graduate Texts in Mathematics, vol. 233 (Springer, New York, 2006)
4.
E. M. Alfsen, Compact Convex Sets and Boundary Integtrals. Ergebnisse der Mathematik und ihrer Granzgebiete, Band 57 (Springer, New York, 1971)
23.
W. G. Bade, The Space of all Continuous Functions on a Compact Hausdorff Space (University of California, Berkeley, 1957). Library call no. QA689.B16
24.
W. G. Bade, The Banach Space C(S). Lecture Note Series, vol. 26 (Matematisk Institut, Aarhus Universitët, Aarhus, 1971)
30.
S. Banach, Théorie des Opérations Linéaires. Monografie Matematyczne, vol. 1 (Instytut Matematyczny Polskiej Akademii Nauk, Warsaw, 1932)
36.
G. Birkhoff, Lattice Theory, 3rd edn. (American Mathematical Society, Providence, 1967)MATH
39.
47.
T. Budak, N. Işik, J. Pym, Minimal determinants of topological centres for some algebras associated with locally compact groups. Bull. London Math. Soc. 43, 495–506 (2011)MathSciNetCrossRefMATH
52.
C. Caratheodory, Die homomorphieen von somen und die multiplikation von inhaltsfunktionen. Annalen Scuola Norm. Sup. Pisa Cl. Sci. 8 (2), 105–130 (1939)MathSciNetMATH
59.
60.
W. W. Comfort, Topological groups, in Handbook of Set Theoretic Topology, ed. by K. Kunen, J.E. Vaughan (North Holland, New York, 1984), pp. 1143–1263CrossRef
68.
H. G. Dales, Banach Algebras and Automatic Continuity. London Mathematical Society Monographs, vol. 24 (Clarendon Press, Oxford, 2000)
71.
H. G. Dales, A. T.-M. Lau, D. Strauss, Banach algebras on semigroups and on their compactifications. Mem. American Math. Soc. 205, 165 (2010)MathSciNetMATH
72.
H. G. Dales, A. T.-M. Lau, D. Strauss, Second duals of measure algebras. Diss. Math. (Rozprawy Matematyczne) 481, 121 (2012)
76.
F. K. Dashiell Jr., Nonweakly compact operators from order-Cauchy complete C(S) lattices, with application to Baire classes. Trans. American Math. Soc. 266, 397–413 (1981)MathSciNetMATH
85.
J. Diestel, J. J. Uhl Jr., Vector Measures. Mathematical Surveys, vol. 15 (American Mathematical Society, Providence, 1977)
91.
J. Dixmier, Sur certains espaces considérés par M. H. Stone. Summa Brasiliensis Math. 2, 151–182 (1951)MathSciNetMATH
94.
N. Dunford, J. T. Schwartz, Linear Operators, Part I: General Theory (Interscience Publishers, New York, 1957)MATH
101.
103.
104.
V. P. Fonf, J. Lindenstrauss, R. R. Phelps, Infinite dimensional convexity, in Handbook of the Geometry of Banach Spaces, vol. 1, ed. by W. B. Johnson, J. Lindenstrauss (North Holland/Elsevier, Amsterdam, 2001), pp. 599–670CrossRef
107.
108.
D. H. Fremlin, G. Plebanek, Large families of mutually singular Radon measures. Bull. Pol. Acad. Sci. Math. 51, 169–174 (2003)MathSciNetMATH
110.
I. M. Gelfand, Abstrakte Functionen und Lineare Operatoren. Recueil Math. 4, 235–286 (1938)MATH
116.
C. Goffman, Real Functions (Prindle/Weber/Schmidt, Boston, 1953)MATH
124.
A. Grothendieck, Sur les appplications lineaires faiblement compactes d’espaces du type C(K). Canadian J. Math. 5, 129–173 (1953)MathSciNetCrossRefMATH
132.
137.
E. Hewitt, K. A. Ross, Abstract Harmonic Analysis I, 2nd edn. (Springer, Berlin, 1979)MATH
138.
E. Hewitt, K. Stromberg, Real and Abstract Analysis (Springer, New York, 1975)MATH
158.
A. Kolmogorov, General measure theory and the calculus of probabilities. Trudy Kommunist Akad. Razd. mat. 8–21 (1929, in Russian). English transl.: Selected works of A. N. Kolmogorov, vol. II, ed. by A. N. Shiryayev (Kluwer Academic Publishers, Dordrecht, 1992), pp. 48–59
166.
167.
A. T.-M. Lau, V. Losert, Complementation of certain subspaces of L ∞ (G) of a locally compact group. Pacific J. Math. 141, 295–310 (1990)MathSciNetCrossRefMATH
168.
178.
J. Lukeš, J. Malý, I. Netuka, J. Spurný, Integral Representation Theory (Walter de Gruyter, Berlin, 2010)MATH
179.
180.
W. A. J. Luxemburg, A. C. Zaanan, Riesz Spaces, vol. I (North Holland, Amsterdam, 1971)
182.
D. Maharam, Decompositions of measure algebras. Proc. Natl. Acad. Sci. USA 28, 142–160 (1942)CrossRefMATH
184.
194.
T. W. Palmer, Banach Algebras and the General Theory of ∗-Algebras, vol. I, Algebras and Banach Algebras (Cambridge University Press, Cambridge, 1994)
195.
T. W.Ṗalmer, Banach Algebras and the General Theory of ∗-Algebras, vol. II, ∗-Algebras (Cambridge University Press, Cambridge, 2001)
196.
A. Pełczyński, On the isomorphism of the spaces m and M. Bull. Acad. Pol. Sci. 6, 695–696 (1958)
197.
198.
A. Pełczyński, Linear extensions, linear averagings, and their applications to linear topological classification of spaces of continuous functions. Diss. Math. (Rozprawy Matematyczne) 63, 92 (1968)
200.
201.
R. Phelps, Lectures on Choquet’s Theorem. van Nostrand Mathematical Studies, vol. 7 (van Nostrand, Princeton, 1966). Second edition, Lecture Notes in Mathematics, vol. 1757 (Springer, Berlin, 2001)
202.
206.
G. Plebanek, A normal measure on a compact connected space. Unpublished notes (2014)
211.
H. P. Rosenthal, On injective Banach spaces and the spaces L ∞ (μ) for finite measures μ. Acta Math. 124, 205–248 (1970)
216.
H. L. Royden, Real Analysis, 3rd edn. (Prentice-Hall, Engelwood Cliffs, 1988)MATH
217.
W. Rudin, Real and Complex Analysis, 3rd edn. (McGraw-Hill, New York, 1986)MATH
218.
W. Rudin, Functional Analysis, 2nd edn. (McGraw-Hill, New York, 1991)MATH
219.
K. Saitô, J. D. M. Wright, C ∗-algebras which are Grothendieck spaces. Rend. Circ. Mat. Palermo, Serie II 52, 141–144 (2003)
220.
K. Saitô, J. D. M. Wright, Monotone Complete C ∗ -Algebras and Generic Dynamics. Springer Monographs in Mathematics (Springer, London, 2015)
224.
225.
Z. Semadeni, Banach Spaces of Continuous Functions. Monografie Matematyczne, vol. 55 (Instytut Matematyczny Polskiej Akademii Nauk, Warsaw, 1971)
233.
E. Szpilrajn, On the space of measurable sets. Annalen Soc. Pol. Math. 17, 120–121 (1938)
234.
Metadata
Title
Measures
Authors
H. G. Dales
F. K. Dashiell Jr.
A. T.-M. Lau
D. Strauss
Copyright Year
2016
Book
Banach Spaces of Continuous Functions as Dual Spaces

Print ISBN: 978-3-319-32347-3

Electronic ISBN: 978-3-319-32349-7

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-32349-7_4

Premium Partner

    Image Credits