Abstract
The present article is one of several continuations of the recent book of the author [1997a] on measure and integration (cited as MI). This work has the aim to restructure the area of the basic extension and representation procedures which produce the central formations of the theory, like measures of different kinds, from the more primitive data which one meets in nature, like elementary contents and elementary integrals. It is a systematization of the new development which started with Kisyński [1968] and Topsøe [1970ab]. Its fundamental concepts are certain kinds of outer and inner premeasures and their outer and inner extensions. In MI and in the subsequent papers of the author [1997b][1999ab] there are numerous applications which show the power of the new development.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Adamski, W. [1982] Tight set functions and essential measure. Lecture Notes Math. 945, 1-14. Springer.
Bassanezi, R.C. and G.H.Greco [1984] Sull’additività dell’integrale. Rend.Sem.Mat.Univ.Padova 72, 249-275.
Bauer, H. [1992] Maß- und Integrationstheorie. 2.Aufl. de Gruyter.
Berg, C., J.R.P.Christensen, and P.Ressel [1984] Harmonic Analysis on Semigroups.Graduate Texts Math. 100. Springer.
Bourbaki, N. [1965] Intèegration. Chap.1-4, 2ième Ed. Hermann.
Bourbaki, N. [1967] Intèegration. Chap.5, 2ième Ed. Hermann.
Cohn, D.L. [1980] Measure Theory.Birkhuser.
Floret, K. [1981] Maß- und Integrationstheorie. Teubner.
Fremlin, D.H. [1975] Topological measure theory: Two counter-examples.Math.Proc.Camb.Phil.Soc. 78, 95-106.
Greco, G.H. [1982] Sulla rappresentazione di funzionali mediante integrali.Rend.Sem.Mat.Univ.Padova 66, 21-42.
Kisyński, J. [1968] On the generation of tight measures. Studia Math. 30,141-151.
Köonig, H. [1997a] Measure and Integration: An Advanced Course in Basic Procedures and Applications. Springer.
Köonig, H. [1997b] Image measures and the so-called image measure catastrophe.Positivity 1, 255-270.
Köonig, H. [1998] Measure and integration: Integral representations of isotonefunctionals. These Annales 9, 123-153.
Köonig, H. [1999a] What are signed contents and measures? Math.Nachr.204, 101-124.
Köonig, H. [1999b] The product theory for inner premeasures. Note di Mat.17(1997), 235-249.
Köonig, H. [1999c] Measure and integration: Comparison of old and new procedures.Arch.Math. 72, 192-205.
Leinert, M. [1995] Integration und Maß.Vieweg.
Loomis, L.H. [1954] Linear functionals and content. Amer.Journ.Math. 76,168-182.
Sapounakis, A. and M.Sion [1983] On generation of Radon like measures. In:Measure Theory and its Applications (Sherbrooke 1982). Lecture Notes Math. 1033, 283-294. Springer.
Sapounakis, A. and M.Sion [1987] Construction of regular measures. These Annales 1, 157-196.
Schwartz, L. [1973]Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures.Oxford Univ.Press.
Topsøe, F. [1970a] Compactness in spaces of measures. Studia Math. 36,195-212.
Topsøe, F. [1970b] Topology and Measure. Lecture Notes Math. 133, Springer.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer Basel
About this chapter
Cite this chapter
König, H. (2012). Measure and Integration: Mutual generation of outer and inner premeasures. In: Measure and Integration. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0382-3_3
Download citation
DOI: https://doi.org/10.1007/978-3-0348-0382-3_3
Received:
Published:
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0381-6
Online ISBN: 978-3-0348-0382-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)