The Radon‐Nikodym property, generalized bounded variation and the average range | Zendy

Kaliaj Sokol Bush | Zendy

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The Radon‐Nikodym property, generalized bounded variation and the average range

Author(s) -

Kaliaj Sokol Bush

Publication year - 2014

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.201300171

Subject(s) - mathematics , bounded variation , bounded function , banach space , property (philosophy) , range (aeronautics) , approximation property , variation (astronomy) , pure mathematics , bounded operator , mathematical analysis , philosophy , materials science , physics , epistemology , astrophysics , composite material

A generalized bounded variation characterization of Banach spaces possessing the Radon‐Nikodym property is given in terms of the average range. We prove that a Banach space X has the Radon‐Nikodym property if and only if for each function F : [ 0 , 1 ] → X of generalized bounded variation on [0, 1], the average rangeA F ( t )is a nonempty set at almost all t ∈ [ 0 , 1 ] .

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