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Analysis and Probability by Aurel Spataru

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Chapter 4

The Integral

The material of Chapter 3 enables us to introduce and study the important notion of integral in this chapter. In Section 11 we define the integral, and we examine remarkable properties of the integral. Section 12 deals with the Radon-Nikodým theorem and with the Lebesgue decomposition. In Section 13 we study the function spaces image, and in Section 14 we define and study three new kinds of convergence for sequences of functions: almost everywhere, in measure and in image.

Throughout this chapter, unless otherwise stated, (X, , ) is ...

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