论文标题
liouville型定理在有限订单的功能的小型杰出集外
Liouville-type theorems outside of small exceptional sets for functions of finite order
论文作者
论文摘要
我们证明，有限顺序上有限顺序的凸功能在有限尺寸的真实空间上的有限顺序函数，从某些零相对Lebesgue密度的外部界定，从任何地方都界定。因此，有限平面上有限顺序，有限顺序的全部和plurisubharmonic函数以及有限顺序的全部和多数式函数以及有限顺序的凸面或谐波函数的次谐波功能是恒定的。
We prove that convex functions of finite order on the real line and subharmonic functions of finite order on finite dimensional real space, bounded from above outside of some set of zero relative Lebesgue density, are bounded from above everywhere. It follows that subharmonic functions of finite order on the complex plane, entire and plurisubharmonic functions of finite order, and convex or harmonic functions of finite order bounded from above outside some set of zero relative Lebesgue density are constant.
