Continuity of the $L_{p}$ Balls and an Application to Input-Output System Described by the Urysohn Type Integral Operator
英文摘要：
In this paper the continuity of the set valued map $p\rightarrow B_{Ω,\mathcal{X},p}(r),$ $p\in (1,+\infty),$ is proved where $B_{Ω,\mathcal{X},p}(r)$ is the closed ball of the space $L_{p}\left(Ω,Σ,μ; \mathcal{X}\right)$ centered at the origin with radius $r,$ $\left(Ω,Σ,μ\right)$ is a finite and positive measure space, $\mathcal{X}$ is separable Banach space. An application to input-output system described by Urysohn type integral operator is discussed.
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