This text contains a basic introduction to the abstract measure theory
and the Lebesgue integral. Most of the standard topics in the measure
and integration theory are discussed. In addition, topics on the
Hewitt-Yosida decomposition, the Nikodym and Vitali-Hahn-Saks theorems
and material on finitely additive set functions not contained in
standard texts are explored. There is an introductory section on
functional analysis, including the three basic principles, which is used
to discuss many of the classic Banach spaces of functions and their
duals. There is also a chapter on Hilbert space and the Fourier
transform.Download
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