Distances to spaces of measurable and integrable functions

Journal ar
Mathematische Nachrichten
  • Volumen: 286
  • Número: 14-15
  • Fecha: 01 October 2013
  • Páginas: 1424-1438
  • ISSN: 0025584X 15222616
  • Source Type: Journal
  • DOI: 10.1002/mana.201200241
  • Document Type: Article
Given a complete probability space (¿,¿,¿) and a Banach space X we establish formulas to compute the distance from a function f¿X¿ to the spaces of strongly measurable functions and Bochner integrable functions. We study the relationship between these distances and use them to prove some quantitative counterparts of Pettis' measurability theorem. We also give several examples showing that some of our estimates are sharp. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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