Synopsis
I Preliminaries.- 1 Set theory.- 2 Linear algebra.- 3 General topology.- 4 Metric spaces.- 5 Complex analysis.- 6 Measurability.- 7 Integrals and measures.- 8 Measure theory.- 9 More integration theory.- 10 Measure and topology.- II Banach Spaces.- 11 Normed linear spaces.- 12 Bounded linear transformations.- 13 The open mapping theorem.- 14 The Hahn-Banach theorem.- 15 Local convexity and weak topologies.- 16 Duality.- 17 Banach spaces and integration theory.- 18 The spaces C(X).- 19 Vector sums and bases.- References to the examples, propositions, and problems.
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