A special case of Vinogradov's mean value theorem
R. C. Vaughan, T. D. Wooley (1997)
Acta Arithmetica
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R. C. Vaughan, T. D. Wooley (1997)
Acta Arithmetica
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E. V. Flynn (1994)
Acta Arithmetica
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Hans Peter Schlickewei, Wolfgang M. Schmidt (1995)
Acta Arithmetica
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Sy Friedman (1997)
Fundamenta Mathematicae
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We present a reformulation of the fine structure theory from Jensen [72] based on his Σ* theory for K and introduce the Fine Structure Principle, which captures its essential content. We use this theory to prove the Square and Fine Scale Principles, and to construct Morasses.
Peter J. Grabner, Pierre Liardet (1999)
Acta Arithmetica
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Matthew J. Klassen, Edward F. Schaefer (1996)
Acta Arithmetica
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W. Jurkat, D. Nonnenmacher (1994)
Fundamenta Mathematicae
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We introduce an axiomatic approach to the theory of non-absolutely convergent integrals. The definition of our ν-integral will be descriptive and depends mainly on characteristic null conditions. By specializing our concepts we will later obtain concrete theories of integration with natural properties and very general versions of the divergence theorem.
Valentin Gutev, Haruto Ohta (2000)
Fundamenta Mathematicae
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The above question was raised by Teodor Przymusiński in May, 1983, in an unpublished manuscript of his. Later on, it was recognized by Takao Hoshina as a question that is of fundamental importance in the theory of rectangular normality. The present paper provides a complete affirmative solution. The technique developed for the purpose allows one to answer also another question of Przymusiński's.