我們研究架構於一般集合族上的 John-Stromberg 不等式，而這個集合族滿足拓樸測度空間上的一些公設條件，包含歐式空間上的嚴格凸函數所衍生的 section 族。也會引進對應的仿射 VMO 空間，並研究該空間的相關性質。有了上述相關結果後，我們就有可能證明局部非退化 Monge-Ampere 方程解的正則理論。 ;We study the John-Stromberg inequality over families of general sets in topological measure spaces satisfying certain axioms, which include families of sections induced by strictly convex functions in $\Bbb R^n$. Affine VMO space is introduced and studied. Then we will present a regularity theory for entire solutions of locally nondegenerate Monge-Ampere equation $\det D^2u=f(x)$ with $f$ in local affine VMO space.
