Convergence theorems for Banach space valued integrable multifunctions

• Nikolaos S. Papageorgiou

  Department of Mathematics, University of California, Davis, California 95616, USA

抄録

In this work we generalize a result of Kato on the pointwise behavior of a weakly convergent sequence in the Lebesgue-Bochner spaces<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$L_X^P \left( \Omega \right)\left( {1 \leqslant p \leqslant \infty } \right)$" id="E1"><mml:msubsup><mml:mi>L</mml:mi><mml:mi>X</mml:mi><mml:mi>P</mml:mi></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mi>Ω</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo> (</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>≤</mml:mo><mml:mi>p</mml:mi><mml:mo>≤</mml:mo><mml:mi>∞</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>. Then we use that result to prove Fatou's type lemmata and dominated convergence theorems for the Aumann integral of Banach space valued measurable multifunctions. Analogous convergence results are also proved for the sets of integrable selectors of those multifunctions. In the process of proving those convergence theorems we make some useful observations concerning the Kuratowski-Mosco convergence of sets.

収録刊行物

• International Journal of Mathematics and Mathematical Sciences

  International Journal of Mathematics and Mathematical Sciences 10 (3), 433-442, 1987

  Hindawi Limited

キーワード

• Mathematics (miscellaneous)

詳細情報

• CRID: 1362544419345945600
• NII論文ID: 30022194155
• DOI: 10.1155/s0161171287000516
• ISSN: 16870425
• ISSN: 01611712
• Web Site: http://downloads.hindawi.com/journals/ijmms/1987/679178.pdf
• データソース種別:
  • Crossref
  • CiNii Articles