任意正测度集上都不可测的函数

A Nonmeasurable Function on Any Posihve Measure Set

本文讨论了函数方程ｆ（ｘ＋ｙ）＝ｆ（Ｘ）＋ｆ（ｙ），的解为线性函数的充要条件，并证明了上方程的非线性解的存在性．由此给出了任意正测度［注］集上都不可测的直线上的函数．

This paper discussed the necessary and suffident condition of the solution of functionalequationf(x+y)=f(x)+f(y)x,y∈Rbe linear functions. Thus it given a nonmeasurable function on any positive measure set.