Continuity properties of the superposition operator

Journal of the Australian Mathematical Society

Jürgen Appell¹ 

[1] Pjotr P. Zabrejko

关键词: 47 H 15;    46 E 30;    26 B 40;    28 A 20;   

DOI  :  10.1017/S1446788700031633

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Various continuity conditions (in norm, in measure, weakly etc.) for the nonlinear superposition operator F x(s) = f(s, x(s)) between spaces of measurable functions are established in terms of the generating function f = f(s, u). In particular, a simple proof is given for the fact that, if F is continuous in measure, then f may be replaced by a function f which generates the same superposition operator F and satisfies the Carathéodory conditions. Moreover, it is shown that integral functional associated with the function f are proved.

【 授权许可】

Unknown