Hüseyin, Anar2023-09-222023-09-2219.07.2023Huseyin, A. On the Vietoris semicontinuity property of the 𝐿𝑝 balls at 𝑝=1 and an application. Arch. Math. 121, 171–182 (2023). https://doi.org/10.1007/s00013-023-01881-yhttps://link.springer.com/article/10.1007/s00013-023-01881-yhttps://hdl.handle.net/20.500.12418/14129In this paper the Vietoris right lower semicontinuity at $p=1$ of the set valued map $p\rightarrow B_{\Omega,\mathcal{X},p}(r)$, $p\in [1,\infty]$, is discussed where $B_{\Omega,\mathcal{X},p}(r)$ is the closed ball of the space $L_{p}(\Omega,\Sigma,\mu; \mathcal{X})$ centered at the origin with radius $r$, $(\Omega,\Sigma,\mu)$ is a finite and positive measure space, $\mathcal{X}$ is a separable Banach space. It is proved that the considered set valued map is Vietoris right lower semicontinuous at $p=1$. Introducing additional geometric constraints on the functions from the ball $B_{\Omega,\mathcal{X},1}(r)$, a property which is close to the Hausdorff right lower semicontinuity, is derived. An application of the obtained result to the set of integrable outputs of the input-output system described by the Urysohn type integral operator is studied.en10.1007/s00013-023-01881-yinfo:eu-repo/semantics/closedAccessVietoris semicontinuity, set valued map, Urysohn integral operator, input-output systemArticle12121821712-s2.0-85165207779N/AWOS:001032567300001Q3