  We study the property of global-local mixing for full-branched expanding maps
of either the half-line or the interval, with one indifferent fixed point.
Global-local mixing expresses the decorrelation of global vs local observables
w.r.t. to an infinite measure $\mu$. Global observables are essentially bounded
functions admitting an infinite-volume average, i.e., a limit for the average
of the function over bigger and bigger intervals; local observables are
integrable functions (both notions are relative to $\mu$). Of course, the
definition of global observable depends on the exact definition of
infinite-volume average. The first choice for it would be to consider averages
over the entire space minus a neighborhood of the indifferent fixed point
(a.k.a. the "point at infinity"), in the limit where such neighborhood
vanishes. This is the choice that was made in previous papers on the subject.
The classes of systems for which global-local mixing was proved, with this
natural choice of global observables, are ample but not really general. In this
paper we consider uniformly global observables, i.e., $L^\infty$ functions
whose averages over any interval $V$ converges to a limit, uniformly as $\mu(V)
\to \infty$. Uniformly global observables form quite an extensive subclass of
all global observables. We prove global-local mixing in the sense of uniformly
global observables, for two truly general classes of expanding maps with one
indifferent fixed point, respectively on $\mathbb{R}_0^+$ and on $(0,1]$. The
technical core of the proofs is rather different from previous work.
