A net x_α in a lattice-normed vector lattice (X, p, E) is unbounded p-convergent to x ∈ X if \(p\left({\left| {{x_\alpha} - x} \right| \wedge u} \right)\buildrel o \over \longrightarrow \) 0 for every u ∈ X₊. This convergence has been investigated recently for (X, p, E) = (X, |·|, X) under the name of uo-convergence, for (X, p, E) = (X, ‖·‖, ℝ) under the name of un-convergence, and also for \(\left({X,\;p,\;{\mathbb{R}^{X^{\prime}}}} \right)\), where p(x)[f]:= |f|(|x|), under the name uaw-convergence. In this paper we study general properties of the unbounded p-convergence.

中文翻译：

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晶格范矢量格的无界p-收敛

净X _α中的格子赋范向量格（X，P，E）是无界p -convergent到X ∈ X如果\（P \左（{\左| {{X_ \阿尔法} - X} \右| \楔ù} \右）\ buildrelø\超过\ longrightarrow \） 0每ü ∈ X ₊。最近，以uo -convergence的名义对（X，p，E）=（X，|·|，X）的这种收敛进行了研究，对于（X，p，E）=（X，”·“，ℝ）以非收敛的名义\（\ left（{X，\; p，\; {\ mathbb {R} ^ {X ^ {\ prime}}}} \ right）\），其中p（x）[ f ]：= | f | （| x |），名称为uaw -convergence。在本文中，我们研究了无界p收敛的一般性质。