We present a novel generalization, in Banach spaces, of the celebrated Helly’s principle selection. Specifically, our main result is a quantitative version of such principle selection. Our main tool is the so called Degree of Nondensifiability, which measures (in the specified sense) the distance of a given convex subset of a Banach space to the class of its Peano Continua. As application of our results, we analyze the solvability of certain Volterra integral equations.

中文翻译：

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Banach空间中Helly选择原理的量化版本及其应用

我们在 Banach 空间中提出了著名的 Helly 原则选择的新颖概括。具体来说，我们的主要结果是这种原则选择的量化版本。我们的主要工具是所谓的不可密度度，它测量（在特定意义上）Banach 空间的给定凸子集与其 Peano Continua 类的距离。作为我们结果的应用，我们分析了某​​些 Volterra 积分方程的可解性。