The Fourier transform of a stationary random measure on an arbitrary locally compact Abelian group is defined and used to extend some results on the representation of homogeneous random fields as moving averages.
"A Note on Random Measures and Moving Averages on Non-discrete Groups." Ann. Probab. 1 (2) 336 - 337, April, 1973. https://doi.org/10.1214/aop/1176996987