Uniform integrability of sequences of random elements with respect to weak topologies and weak integrals

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Uluçay H., ÜNVER M.

Hacettepe Journal of Mathematics and Statistics, cilt.52, sa.1, ss.91-102, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 52 Sayı: 1
  • Basım Tarihi: 2023
  • Doi Numarası: 10.15672/hujms.1065594
  • Dergi Adı: Hacettepe Journal of Mathematics and Statistics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.91-102
  • Anahtar Kelimeler: weak uniform integrability, statistical convergence, strong convergence
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

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.