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Spectral orders, uniform integrability and Lebesgue's dominated convergence theorem
1974
Transactions of the American Mathematical Society
Preserved Fulltext
Using the 'spectral' order relations < and -K introduced by Hardy, Littlewood and Pólya, we characterize the uniform integrability of a family of integrable functions. We also prove an extension and a 'converse' of the classical Lebesgue's dominated convergence theorem in terms of the 'spectral' orders < and •«.
doi:10.1090/s0002-9947-1974-0369646-2
fatcat:vlnfivbmwbe6peqqktp5n7akra