Let be a positive definite, measurable function on the Interval
. Then there exists a monotone
increasing, real-valued bounded function such that

for ``Almost All'' . If is nondecreasing and bounded and is defined as above, then is called the Fourier-Stieltjes transform of , and is both continuous and positive definite.

**References**

Iyanaga, S. and Kawada, Y. (Eds.). *Encyclopedic Dictionary of Mathematics.*
Cambridge, MA: MIT Press, p. 618, 1980.

© 1996-9

1999-05-26