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A Theorem of Menšov on the Adjustment of Functions
Author(s) -
Körner T. W.
Publication year - 1999
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610799007899
Subject(s) - fourier series , mathematics , series (stratigraphy) , trigonometric series , representation (politics) , function (biology) , function series , pure mathematics , set (abstract data type) , trigonometric functions , measurable function , conjugate fourier series , mathematical analysis , fourier transform , fourier analysis , computer science , geometry , paleontology , evolutionary biology , politics , political science , law , bounded function , biology , programming language , short time fourier transform
A new proof is given of a theorem of Menšov which states that a measurable function can be changed on a set of arbitrarily small measure to obtain a function with uniformly convergent Fourier series. Other results of Menšov on the representation of functions by trigonometric series are obtained by using a related result.