In this chapter, topological groups and invariant integration are introduced. The existence of a translation invariant measure on a locally compact group, called Haar measure, gives the very basic tool for the Harmonic Analysis on such groups. The Harmonic Analysis of a group is basically concerned with the study of measurable functions on the group, in particular the spaces L1(G) and L2(G), both taken with respect to Haar measure. The invariance of this measure allows to analyze these function spaces by some generalized Fourier Analysis, and we shall see in further chapters of this book how powerful these techniques are.
KeywordsTopological Group Compact Group Haar Measure Radon Measure Modular Function
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