有界变差分离弱和强平均利普希茨。

IF 2 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Entropy Pub Date : 2025-09-18 DOI:10.3390/e27090974

Ariel Elperin, Aryeh Kontorovich

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引用次数: 0

摘要

我们仔细研究了最近引入的平均平滑的概念。后者定义了一般度量空间上实值函数的弱和强平均- lipschitz半模。对于实线上的标准度量，我们将这些概念与有界变差（BV）进行比较，发现弱概念严格弱于BV，而强概念严格强。在此过程中，我们发现弱平均平滑类在某种组合意义上也相当大，这是由fat-shattering维度精确实现的。

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Bounded Variation Separates Weak and Strong Average Lipschitz.

We closely examine a recently introduced notion of average smoothness. The latter defined a weak and strong average-Lipschitz seminorm for real-valued functions on general metric spaces. Specializing to the standard metric on the real line, we compare these notions to bounded variation (BV) and discover that the weak notion is strictly weaker than BV while the strong notion is strictly stronger. Along the way, we discover that the weak average smooth class is also considerably larger in a certain combinatorial sense, which is made precise by the fat-shattering dimension.

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来源期刊

Entropy PHYSICS, MULTIDISCIPLINARY-

CiteScore

4.90

自引率

11.10%

发文量

1580

审稿时长

21.05 days

期刊介绍： Entropy (ISSN 1099-4300), an international and interdisciplinary journal of entropy and information studies, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish as much as possible their theoretical and experimental details. There is no restriction on the length of the papers. If there are computation and the experiment, the details must be provided so that the results can be reproduced.