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Distances to spaces of measurable and integrable functions
Author(s) -
Angosto C.,
Cascales B.,
Rodríguez J.
Publication year - 2013
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200241
Subject(s) - mathematics , integrable system , measurable function , banach space , locally integrable function , pure mathematics , space (punctuation) , function space , function (biology) , mathematical analysis , interpolation space , functional analysis , linguistics , philosophy , biochemistry , chemistry , evolutionary biology , gene , bounded function , biology
Given a complete probability space ( Ω , Σ , μ ) and a Banach space X we establish formulas to compute the distance from a function f ∈ X Ωto 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.