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Egoroff, σ, and convergence properties in some archimedean vector lattices

A. W. Hager, J. van Mill (2015)

Studia Mathematica

An archimedean vector lattice A might have the following properties: (1) the sigma property (σ): For each a n c o n A there are λ n ( 0 , ) and a ∈ A with λₙaₙ ≤ a for each n; (2) order convergence and relative uniform convergence are equivalent, denoted (OC ⇒ RUC): if aₙ ↓ 0 then aₙ → 0 r.u. The conjunction of these two is called strongly Egoroff. We consider vector lattices of the form D(X) (all extended real continuous functions on the compact space X) showing that (σ) and (OC ⇒ RUC) are equivalent, and equivalent...

Embedding c 0 in bvca ( Σ , X )

Juan Carlos Ferrando, L. M. Sánchez Ruiz (2007)

Czechoslovak Mathematical Journal

If ( Ω , Σ ) is a measurable space and X a Banach space, we provide sufficient conditions on Σ and X in order to guarantee that b v c a ( Σ , X ) , the Banach space of all X -valued countably additive measures of bounded variation equipped with the variation norm, contains a copy of c 0 if and only if X does.

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