关于Lebesgue函数空间的左右极限空间L^(p-0)[0,1]和L^(p+0)[0,1]

Left and Right Limit Spaces L^(p-0)[0,1] and L^(p+0)[0,1] of the Lebesgue Function Space

刻画了经典函数Banach空间Lp[0,1]的左右极限空间Lp-0[0,1]和Lp+0[0,1]空间,发现Lp-0[0,1]是不可赋范的局部凸的可分的Fréchet空间,Lp+0[0,1]是不可度量的有界完备的局部凸的桶的Hausdorff空间.

In classical function mal and is a loca a vector space,the left limit space L^p-0[0,1] and right limit space L^p＋0[0,1] of the Banach spaces about L^p[0,1] are described. It is found that L^p-0[0,1] is not norlly convex separated Frechet space,L^p＋0[0,1] is not metric and is a bounded cornplete bornological locally convex Hausdorff space.