Abstract
Given a measure μ on a measurable space \(S,\mathcal{A}\), we now define the integral for arbitrary measurable functions
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Notes
- 1.
Andrei Markov, 1856–1922, born in Ryazan, active in St. Petersburg. He is mainly known for his fundamental contributions to probability theory.
- 2.
Beppo Levi, 1875–1961, born in Turin, active in Piacenza, Cagliari, Parma, Bologna, and Rosario. He wrote papers in areas as distinct as algebraic geometry, set theory, integration theory, projective geometry, and number theory. Because of his Jewish origin he went into exile to Argentina in 1939.
- 3.
Pierre Fatou, 1878–1929, born in Lorient, active as astronomer at the Paris observatory. To him we owe applications of Lebesgue integration to Fourier series and complex analysis.
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Brokate, M., Kersting, G. (2015). The Integral of Nonnegative Functions. In: Measure and Integral. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-15365-0_4
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