دورية أكاديمية
A generalization of Fatou’s lemma for extended real-valued functions on σ-finite measure spaces: with an application to infinite-horizon optimization in discrete time
| العنوان: | A generalization of Fatou’s lemma for extended real-valued functions on σ-finite measure spaces: with an application to infinite-horizon optimization in discrete time |
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| المؤلفون: | Takashi Kamihigashi |
| المصدر: | Journal of Inequalities and Applications, Vol 2017, Iss 1, Pp 1-15 (2017) |
| بيانات النشر: | SpringerOpen, 2017. |
| سنة النشر: | 2017 |
| المجموعة: | LCC:Mathematics |
| مصطلحات موضوعية: | Fatou’s lemma, σ-finite measure space, infinite-horizon optimization, hyperbolic discounting, existence of optimal paths, Mathematics, QA1-939 |
| الوصف: | Abstract Given a sequence { f n } n ∈ N $\{f_{n}\}_{n \in \mathbb {N}}$ of measurable functions on a σ-finite measure space such that the integral of each f n $f_{n}$ as well as that of lim sup n ↑ ∞ f n $\limsup_{n \uparrow\infty} f_{n}$ exists in R ‾ $\overline{\mathbb {R}}$ , we provide a sufficient condition for the following inequality to hold: lim sup n ↑ ∞ ∫ f n d μ ≤ ∫ lim sup n ↑ ∞ f n d μ . $$ \limsup_{n \uparrow\infty} \int f_{n} \,d\mu\leq \int\limsup_{n \uparrow\infty} f_{n} \,d\mu. $$ Our condition is considerably weaker than sufficient conditions known in the literature such as uniform integrability (in the case of a finite measure) and equi-integrability. As an application, we obtain a new result on the existence of an optimal path for deterministic infinite-horizon optimization problems in discrete time. |
| نوع الوثيقة: | article |
| وصف الملف: | electronic resource |
| اللغة: | English |
| تدمد: | 1029-242X 43541585 |
| العلاقة: | http://link.springer.com/article/10.1186/s13660-016-1288-5Test; https://doaj.org/toc/1029-242XTest |
| DOI: | 10.1186/s13660-016-1288-5 |
| الوصول الحر: | https://doaj.org/article/0797f646d4a94f8dba95a2f43541585dTest |
| رقم الانضمام: | edsdoj.0797f646d4a94f8dba95a2f43541585d |
| قاعدة البيانات: | Directory of Open Access Journals |
Full Text Finder | تدمد: | 1029242X 43541585 |
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| DOI: | 10.1186/s13660-016-1288-5 |