<p> Let G be a locally compact group (= locally compact Hausdorff topological group). By the measure algebra of G we mean the Banach *-algebra M(G) of bounded regular Borel measures on G. The major results of this work are a structure theorem for norm decreasing isomorphisms of measure algebras, and a characterization of those Banach algebras which are isometric and isomorphic to the measure algebra of some locally compact group. We also obtain some results on subalgebras of M(G) and on representations of G.</p> / Thesis / Doctor of Philosophy (PhD)

Leung, Cheung Yu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 85-86). / Abstracts in English and Chinese. / Introduction --- p.6 / Chapter 1 --- Preliminaries --- p.7 / Chapter 1.1 --- Locally compact groups and unitary representations --- p.7 / Chapter 1.2 --- Positive definite functions --- p.10 / Chapter 1.3 --- Affine isometric actions of groups --- p.23 / Chapter 1.4 --- Ultraproducts --- p.29 / Chapter 2 --- Amenability --- p.33 / Chapter 2.1 --- Reiter's property --- p.33 / Chapter 2.2 --- Fφlner's property --- p.41 / Chapter 3 --- Kazhdan's Property (T) --- p.43 / Chapter 3.1 --- Definition and basic properties --- p.43 / Chapter 3.2 --- Property (FH) --- p.51 / Chapter 3.3 --- Spectral criterion for Property (T) --- p.56 / Chapter 3.4 --- Property (T) for SL3(Z) --- p.60 / Chapter 3.5 --- Expanders --- p.72 / Approximation Properties of Groups --- p.5 / Chapter 4 --- Haagerup Property --- p.74 / Chapter 4.1 --- Equivalent formulations of Haagerup Property --- p.74 / Chapter 4.2 --- Trees and wall structures --- p.82 / Bibliography --- p.85

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Thesis (M. Sc.)--University of Adelaide, Dept of Pure Mathematics,1984. / Includes bibliographical references (leaves 69-72).

Thesis (Ph. D.)--University of Adelaide, Dept. of Pure Mathematics, 1984. / Includes bibliographical references.

Proefschrift--Eindhoven. / "Stellingen": [6] p. inserted. Summary in Dutch. Bibliography: p. 77-78.

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We look from a new point of view at the definition and basic properties of the Lebesgue measure and integral on Euclidean spaces, on abstract spaces, and on locally compact Hausdorff spaces. We use mini sums to give all of them a unified treatment that is more efficient than the standard ones. We also give Fubini's theorem a proof that is nicer and uses much lighter technical baggage than the usual treatments.