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Invariant functionals, measures, and integrals are a vital tool in studying representations of locally compact groups and in establishing the detailed structure of locally compact Abelian groups. They also provide the function algebras and function spaces that are studied in harmonic analysis. The subject of invariant functionals is large, and we cannot treat it with any completeness. In §15, we construct the Haar integral, which is essential for all of our subsequent work. In §16, we give some technical but interesting facts about Haar measure, and in §§17 and 18, we follow some interesting byways.
KeywordsCompact Group Pairwise Disjoint Haar Measure Modular Function Cardinal Number
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