Compactly uniform Bochner integrability of random elements

ÜNVER M., Uluçay H.

POSITIVITY, cilt.21, sa.4, ss.1261-1272, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21 Sayı: 4
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1007/s11117-017-0465-1
  • Dergi Adı: POSITIVITY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1261-1272
  • Anahtar Kelimeler: Strong convergence, Statistical convergence, Uniform integrability, WEIGHTED SUMS, CONVERGENCE, SUMMABILITY
  • Ankara Üniversitesi Adresli: Evet

Özet

As the concept of uniform integrability has an essential role in the convergence of moments and martingales in the probability theory it is important to study this concept. In the present paper using Bochner integral we define a new type of uniform integrability for sequences of random elements. We give some independent necessary and sufficient conditions for this concept. We also generalize the concepts of strong and statistical convergences to sequences of random elements and we obtain the relationship between these two important concepts of summability theory via this new type of uniform integrability.