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The Riemann‐Lebesgue property is equivalent to the complete continuity property
Author(s) -
Ivakhno Yevgen
Publication year - 2007
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdm039
Subject(s) - converse , mathematics , lebesgue integration , property (philosophy) , lebesgue's number lemma , pure mathematics , riemann integral , lebesgue–stieltjes integration , space (punctuation) , riemann hypothesis , mathematical analysis , geometry , philosophy , epistemology , operator theory , fourier integral operator , linguistics
It is known that every space with the complete continuity property also has the Riemann–Lebesgue property. It turns out that the converse implication is also valid.