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a-algebra AccL Appendix approach to Yang-Mills assumptions BccB+ cluster property Comm compact support connection form continuous function convergence convex function correlation inequalities cos(m countable number countable set coupling constant D.L.R. equations defined Definition denotes differential forms estimate exists extreme Gibbs field strength Field Theory finite range finite support fl(A follows free Euclidean function f function on fl Furthermore gauge invariant Gibbs state ft Gross Hence independent infinite dimensional informal description informal expression integral interaction potential 1P k-cells k-form lattice approximation lattice gauge theories lattice spacing Lemma Let f Let h lldj Math measurable function measure ft Michigan preprint non-abelian non-negative normalization constant notation Pfister phase cell approach Phys positively oriented probability measure proof of Theorem Proposition 4.2.1 quantum mechanical Schwinger-Dyson equations sup-norm tangent functional thermodynamic limit translation and 90°-rotation translation invariant Gibbs valued test vector Wilson-loop variables Yang-Mills theory zero