Abstract
Measure theory is the difficult part of developing the Lebesgue integral. Now that we have a measure space (X, ℐ, μ) at our disposal, we are going to define the integral for measurable functions on X with real or complex values. Here and in the rest of the book, when we speak of a function we will mean a measurable function; most of the time we will not mention specifically that the function is measurable. This lesson contains the elementary properties of the Lebesgue integral, including a statement of the monotone convergence theorem.
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© 1999 Springer Science+Business Media New York
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Gasquet, C., Witomski, P. (1999). Integrating Measurable Functions. In: Fourier Analysis and Applications. Texts in Applied Mathematics, vol 30. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1598-1_13
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DOI: https://doi.org/10.1007/978-1-4612-1598-1_13
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7211-3
Online ISBN: 978-1-4612-1598-1
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