Spectral orders, uniform integrability and Lebesgue’s dominated convergence theorem
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- by Kong Ming Chong PDF
- Trans. Amer. Math. Soc. 191 (1974), 395-404 Request permission
Abstract:
Using the ’spectral’ order relations $\prec$ and $\prec \prec$ 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 $\prec$ and $\prec \prec$.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 191 (1974), 395-404
- MSC: Primary 28A25
- DOI: https://doi.org/10.1090/S0002-9947-1974-0369646-2
- MathSciNet review: 0369646