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Further Theorems concerning Functions of Classes a etc
The Existence of Functions Minimizing Certain Multiple
4 other sections not shown
$2 on G absolutely continuous additive set function Banach boundary values bounded region C(Pi C(Po calculus of variations cell chap chapter class $2 class ty coefficient completely additive set condition on G conditions with exponent continuous on G converge weakly convex function convex set defined definition denote depends derivatives dxdy equicontinuous equivalent everywhere exist numbers existence theory following theorem function of class G and satisfy G and vanishes Green's theorem Haar's lemma Hence holds inequality interior to G Lebesgue integral Lebesgue-Stieltjes integral Let G lim inf linear lower semicontinuity measurable functions order to prove potential proof rectangles region G satisfies a condition satisfies a uniform satisfies the conditions satisfy uniform Holder sequence statement tend weakly tends to zero theorem 2.1 Tonelli uniform convergence uniform Holder conditions uniform Lipschitz condition uniformly bounded vanishes on G variables vector functions weak convergence