关于函数空间完备性的研究

Study on the Completion of Functional Space

主要讨论连续函数空间、可积函数空间的完备性,并得出了连续函数空间的完备性取决于距离d(x,y);Riemann可积函数空间是不完备的,Lebesgue可积函数空间是完备的.在此基础上论述了不完备的函数空间完备化问题.

In this paper, we focused on the complection of space of continuous function; Space of integrable function, and obtaining results that the completion of a continuous function space depends on the distance d （x,y）. Riemann integrable function space is not complete,Lebesgue integrable function space is complete. On this basis,the function of the incompleteness is discussed.