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Lp-Spaces and the Radon-Nikodym Theorem

Part of the Universitext book series (UTX)

In this chapter, we study the spaces of functions whose pth power is integrable. In Section 7.2, we first derive some of the important inequalities (Hölder, Minkowski, Jensen) and then in Section 7.3 investigate the case p = 2 in more detail. Apart from the inequalities, the important results for probability theory are Lebesgue’s decomposition theorem and the Radon-Nikodym theorem in Section 7.4. At first reading, some readers might wish to skip some of the more analytic parts of this chapter.

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© Springer-Verlag London Limited 2008

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