![]() ![]() Moreover, a c-totally minimal group that is either complete solvable or strongly compactly covered must be compact. Applying this result, we prove that a locally compact group G is c-totally minimal if and only if its connected component c(G)c(G) is compact and G/c(G)G/c(G) is c-totally minimal. It is shown that a topological group G is c-(totally) minimal if and only if G has a compact normal subgroup N such that G/NG/N is c-(totally) minimal. Using a well-known theorem of and a characterization of a certain class of Lie groups, due to, we prove that a c-minimal locally solvable Lie group is compact. We show that a locally compact c-minimal connected group is compact. In this paper, we study topological groups having all closed subgroups (totally) minimal and we call such groups c-(totally) minimal. We will establish the boundedness of the Fourier multiplier operator TmfT_ does not admit any infinite orthogonal set of exponential functions by classifying the values of ρ. Extending Loomis’ integration theory for finitely additive measures, it is proved that, modulo null functions, each integrable function can be represented by a unique continuous function on the Stone space. Therefore, they admit a natural embedding into a group of extended real-valued continuous functions on an extremally disconnected compact space, the Stone space of the measurable algebra. All structure groups of measurable algebras arising in a classical context are archimedean. Accordingly, we exhibit a fundamental group of X, with stably closed subgroups corresponding to a special class of measures with X as target. On the other hand, any measurable algebra X is shown to be the range of an essentially unique measure on a measurable space, which plays the role of a universal covering. Each measurable algebra embeds into its structure group, an abelian group with a compatible lattice order, and each (general) measure extends uniquely to a monotone group homomorphism between the structure groups. The domain and range of any measure is a commutative L -algebra. Measure and integration theory for finitely additive measures, including vector-valued measures, is shown to be essentially covered by a class of commutative L -algebras, called measurable algebras. Web of Science - Science Citation Index Expanded.Web of Science - Science Citation Index.Web of Science - Current Contents/Physical, Chemical and Earth Sciences.Ulrich's Periodicals Directory/ulrichsweb.KESLI-NDSL (Korean National Discovery for Science Leaders).Journal Citation Reports/Science Edition.Japan Science and Technology Agency (JST).CNKI Scholar (China National Knowledge Infrastructure).Forum Mathematicum is covered by the following services: ![]()
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