处处不连续又不可测的达布函数类的势

On the Cardinality of the Class of Nonmeasurable and Discontinuous Darboux Functions

该文提出了一种构造处处不连续，而且在任何区间内取到任一函数值ｃ次的达布函数类的新方法，证明了该函数类的势为２＾ｃ（ｃ为连续统势）；还得到了处处不连续又不可测的达布函数类的势为２＾ｃ。

This paper presents a new method constructing the class of Darboux functions which are discontinuous everywhere and take on every function value c times in every interval. The cardinality of the class is proved to be 2c, where c denotes the cardinality of the continuum. A new result can be obtained, cardinality of the class of Darboux functions which are nonmeasurable and discontinous everywhere is 2c.