Proves existence of large vector subspaces and algebras in the families of sequences converging pointwise a.e. but not almost uniformly, and almost uniformly but not uniformly a.e., under natural assumptions.
Nielsen,An Introduction to Integration and Measure Theory, Canadian Mathematical So- ciety Series of Monographs and Advanced Texts, Wiley, New York
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Almost uniform vs. pointwise convergence from a linear point of view
Proves existence of large vector subspaces and algebras in the families of sequences converging pointwise a.e. but not almost uniformly, and almost uniformly but not uniformly a.e., under natural assumptions.