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Integrierbare Funktionen

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Maß und Integral

Part of the book series: Mathematik Kompakt ((MAKO,volume 0))

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Zusammenfassung

Die Integration von messbaren Funktionen \( f:\mathcal{S} \to \mathbb{R} \) führt man auf die Integration von nichtnegativen messbaren Funktionen zurück. Dazu zerlegen wir f in Positiv- und Negativteil:

$$ f = f^ + - f^ - , f^ + : = max \left( {f,0} \right) und f^ - : = max \left( { - f,0} \right). $$

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Authors and Affiliations

  1. Fakultät für Mathematik, Technische Universität München, Boltzmannstr. 3, 85747, Garching bei München

    Martin Brokate

  2. Institut für Mathematik, Goethe-Universität Frankfurt, Robert-Mayer-Strasse 10, 60325, Frankfurt am Main

    Götz Kersting

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  1. Martin Brokate
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  2. Götz Kersting
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© 2011 Springer Basel AG

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Brokate, M., Kersting, G. (2011). Integrierbare Funktionen. In: Maß und Integral. Mathematik Kompakt, vol 0. Springer, Basel. https://doi.org/10.1007/978-3-0346-0646-2_5

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