  The evaluation of the numerically dominant pseudoscalar-pole contribution to
hadronic light-by-light scattering in the muon g-2 involves the
pseudoscalar-photon transition form factor F_{P gamma^* gamma^*}(-Q_1^2,
-Q_2^2) with P = pi^0, eta, eta^\prime and, in general, two off-shell photons
with spacelike momenta Q_{1,2}^2. We show, in a largely model-independent way,
that for pi^0 (eta, eta^\prime) the region of photon momenta below about 1
(1.5) GeV gives the main contribution to hadronic light-by-light scattering. We
then discuss how the precision of current and future measurements of the
single- and double-virtual transition form factor in different momentum regions
impacts the precision of a data-driven estimate of this contribution to
hadronic light-by-light scattering. Based on Monte Carlo simulations for a
planned first measurement of the double-virtual form factor at BESIII, we find
that for the pi^0, eta, eta^\prime-pole contributions a precision of 14\%,
23\%, 15\% seems feasible. Further improvements can be expected from other
experimental data and also from the use of dispersion relations for the
different form factors themselves.
