关于α次hlder条件的性质研究

Some research on the quality of α hlder conditions quality

首先,证明α次hlder条件在四则运算、绝对值运算、数量乘法等运算中仍然成立.其次,结合相关的定义,证明α次hlder条件只是一致连续、绝对连续、有界变差的充分条件,通过相关文献及其反例得出必要性不成立.之后,证明α次hlder条件关于区间的可加性与一致收敛函数列情形下仍然成立.最后,证明在特定前提条件下,Stieltjes积分与Lebesgue积分的等价关系,以及满足α次hlder条件的一个充分必要条件.

First,the α hlder condition in four operations,absolute value operation,and scalar multiplication still established. Secondly,according to the relevant definitions,prove that the α hlder condition is the sufficient conditions of uniformly continuous,absolutely continuous,and bounded variation,and the necessary condition is establishment through the related literature and counterexamples. Thirdly,on a range of additivity and uniform convergence of function,the α hlder condition still holds. Finally,prove that the equivalent relation between the Stieltjes Integral and Lebesgue in certain conditions,and a necessary and sufficient condition of α hlder condition.