We introduce a space of distributional one-forms Ωα1 on the
torus T2 for which holonomies along axis paths are well-defined and
induce H\"older continuous functions on line segments. We show that there
exists an Ωα1-valued random variable A for which Wilson loop
observables of axis paths coincide in law with the corresponding observables
under the Yang-Mills measure in the sense of L\'evy (2003). It holds
furthermore that Ωα1 embeds into the H\"older-Besov space
Cα−1 for all α∈(0,1), so that A has the correct
small scale regularity expected from perturbation theory. Our method is based
on a Landau-type gauge applied to lattice approximations.Comment: 37 pages, 4 figures. Minor revisions. To appear in Communications in
Mathematical Physic