Abstract
In this chapter we discuss under which circumstances measures and functions have densities.
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Notes
- 1.
Johann Radon, 1887–1956, born in Tetschen, active a.o. in Hamburg, Breslau, and Vienna. His working areas were measure and integration theory, functional analysis, calculus of variations, and differential geometry.
- 2.
Otton Nikodým, 1887–1974, born in Zablotow, active in Kraków, Warsaw and at Kenyon College, Ohio. He worked on measure theory and functional analysis.
- 3.
Hans Hahn, 1879–1934, born in Vienna, active in Chernovitz, Bonn, and Vienna. He made essential contributions to functional analysis, measure theory, and real analysis. He played a leading role in the Vienna Circle, a group of positivist philosophers and scientists.
- 4.
Georg Cantor, 1845–1918, born in St. Petersburg, active in Halle. He was the founder of set theory.
Bibliography
H. Bauer, Measure and Integration Theory (de Gruyter, Berlin/New York, 2001)
J. Elstrodt, Maß- und Integrationstheorie, 6. Aufl. (Springer, 2009)
L.C. Evans, R.F. Gariepy, Measure Theory and Fine Properties of Functions (CRC, Boca Raton, 1992)
P.R. Halmos, Measure Theory (Van Nostrand, New York, 1950/Springer, New York, 1974)
A. Klenke, Probability Theory, 2nd edn. (Springer, London/New York, 2013)
A. Pietsch, History of Banach Spaces and Linear Operators (Springer, London, 2007)
W. Rudin, Principles of Mathematical Analysis, 3rd edn. (McGraw-Hill, New York, 1976)
W. Rudin, Real and Complex Analysis, 3rd edn. (McGraw-Hill, Singapore, 1986)
R. Schilling, Measures, Integrals and Martingales (Cambridge University Press, Cambridge/New York, 2005)
The MacTutor history of mathematics archive, http://www-history.mcs.st-and.ac.uk/
D. Werner, Funktionalanalysis, 6. Aufl. (Springer, 2007)
D. Werner, Einführung in die Höhere Analysis, 2. Aufl. (Springer, 2009)
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Brokate, M., Kersting, G. (2015). Absolute Continuity. In: Measure and Integral. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-15365-0_9
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DOI: https://doi.org/10.1007/978-3-319-15365-0_9
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