  We introduce general regular variation, a theory of regular variation
containing the existing Karamata, Bojanic-Karamata/de Haan and Beurling
theories as special cases. The unifying theme is the Popa groups of our title
viewed as locally compact abelian ordered topological groups, together with
their Haar measure and Fourier theory. The power of this unified approach is
shown by the simplification it brings to the whole area of quantifier
weakening, so important in this field.
