- Hacettepe Journal of Mathematics and Statistics
- Vol: 52 Issue: 1
- Uniform integrability of sequences of random elements with respect to weak topologies and weak integ...
Uniform integrability of sequences of random elements with respect to weak topologies and weak integrals
Authors : Havva Uluçay, Mehmet Ünver
Pages : 91-102
Doi:10.15672/hujms.1065594
View : 14 | Download : 4
Publication Date : 2023-02-15
Article Type : Research
Abstract :In probability theory, uniform integrability of families of random variables or random elements plays an important role in the mean convergence. In this paper, we introduce a new version of uniform integrability for sequences in normed spaces in the weak sense. We study the relationship of this new concept with summability theory by considering statistical convergence. We also define a new type of uniform integrability of random elements taking values in topological vector spaces by considering weak integrals. Moreover, we study the connection of summability theory with this new concept as well.Keywords : weak uniform integrability, statistical convergence, strong convergence