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Journal of the London Mathematical Society 1999 60(2):548-560; doi:10.1112/S0024610799007899
© 1999 by London Mathematical Society
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© The London Mathematical Society

A Theorem of Mensov on the Adjustment of Functions

T. W. Körner

DPMMS 16 Mill Lane, Cambridge twk{at}dpmms.cam.ac.uk

Received 12 February 1996. Revision received 11 January 1998.

A new proof is given of a theorem of Mensov 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 Mensov on the representation of functions by trigonometric series are obtained by using a related result.


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