发表机构
Istanbul University; Community College of Philadelphia; University of New Hampshire（伊斯坦布尔大学; 费城社区学院; 新罕布什尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究 Stieltjes 时钟下 Hölder 选择的存在性，证明一致不连通性（等价于一致跳跃支配性）是紧值 g-Hölder 多值函数存在 g-Hölder 选择的充要条件，并揭示跳跃大小分布对选择性质的决定作用。
AI 中文摘要
已知对于满足 0 < α < 1 的普通 Hölder 多值函数，仅靠 Hölder 正则性并不能保证 Hölder 选择的存在性，而且一般情况下甚至连续选择也可能不存在。我们研究当通过 Stieltjes 时钟测量参数时，这种情况如何变化。对于 0 < α < 1，我们刻画了使得每个紧值 g-Hölder 多值函数都承认 g-Hölder 选择的时钟。决定条件为时钟像 Im(g) 的一致不连通性。对于左连续且非降的时钟，该条件等价于一致跳跃支配性：每个正的时钟增量都包含一个跳跃，该跳跃携带该增量的固定正比例。在此条件下，可以通过图的任意指定点选择选择，并对其 Hölder 正则性进行显式控制。反之，当条件不成立时，存在一个紧值 g-Hölder 多值函数没有 g-Hölder 选择。结果表明，选择性质并非简单地由跳跃的存在决定，而是由跳跃大小在尺度上的分布方式决定。
英文摘要
It is known that, for ordinary Hölder multifunctions with 0 < α < 1, Hölder regularity alone does not guarantee the existence of a Hölder selection, and in general even a continuous selection may fail to exist. We ask how this situation changes when the parameter is measured through a Stieltjes clock. For 0 < α < 1, we characterize the clocks for which every compact-valued g-Hölder multifunction admits a g-Hölder selection. The determining condition is uniform disconnectedness of the clock image Im(g). For left-continuous and nondecreasing clocks, this condition is equivalent to uniform jump dominance: every positive clock increment contains a jump carrying a fixed positive fraction of that increment. Under this condition, a selection can be chosen through any prescribed point of the graph, with explicit control of its Hölder regularity. Conversely, when the condition fails, there exists a compact-valued g-Hölder multifunction with no g-Hölder selection. The results show that the selection property is governed not simply by the presence of jumps, but by how their sizes are distributed across scales.
Comments17 pages; no figures or table
