Abstract
Integration of measurable functions \( \mathrm{f}:\mathrm{S}\to \bar{\mathrm{\mathbb{R}}} \) is reduced to integration of nonnegative measurable functions as follows.
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Notes
- 1.
Otto Hölder, 1859–1937, born in Stuttgart, active in Göttingen and Tübingen. He gave important contributions, in particular to group theory.
- 2.
Augustin-Louis Cauchy, 1789–1857, born in Paris, active in Paris at the École Polytechnique and the Collège de France. He is a pioneer of real and complex analysis, all the way from the foundations to applications.
- 3.
Hermann Amandus Schwarz, 1843–1921, born in Hermsdorf, Silesia, active in Zürich, Göttingen, and Berlin. His most important contributions pertain conformal mappings and the calculus of variations.
- 4.
Johan Jensen, 1859–1925, born in Nakskov, active in Copenhagen for the Bell Telephone Company. He also contributed to complex analysis.
- 5.
Bernhard Riemann, 1826–1866, born in Breselenz near Hannover, active in Göttingen. His famous publications are concerned, in particular, with complex analysis, geometry, and number theory.
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Brokate, M., Kersting, G. (2015). Integrable Functions. In: Measure and Integral. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-15365-0_5
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DOI: https://doi.org/10.1007/978-3-319-15365-0_5
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