تقرير
Binary sequences with a Ces\`aro limit
| العنوان: | Binary sequences with a Ces\`aro limit |
|---|---|
| المؤلفون: | Keith, Jonathan M., Markowsky, Greg |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Functional Analysis, 28C99, 28A12 |
| الوصف: | The Ces\`aro limit - the asymptotic average of a sequence of real numbers - is an operator of fundamental importance in probability, statistics and mathematical analysis. To better understand sequences with Ces\`aro limits, this paper considers the space $\mathcal{F}$ comprised of all binary sequences with a Ces\`aro limit, and the associated functional $\nu: \mathcal{F} \rightarrow [0,1]$ mapping each such sequence to its Ces\`aro limit. The basic properties of $\mathcal{F}$ and $\nu$ are enumerated, and chains (totally ordered sets) in $\mathcal{F}$ on which $\nu$ is countably additive are studied in detail. The main result of the paper concerns a structural property of the pair $(\mathcal{F},\nu)$, specifically that $\mathcal{F}$ can be factored (in a certain sense) to produce a monotone class on which $\nu$ is countably additive. In the process, a slight generalisation and clarification of the monotone class theorem for Boolean algebras is proved. Comment: arXiv admin note: substantial text overlap with arXiv:2104.08705 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2107.01020 |
| رقم الأكسشن: | edsarx.2107.01020 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |