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Currently displaying 1 – 4 of 4

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Product measurability and Scorza-Dragoni's type property

Wojciech Zygmunt — 1988

Rendiconti del Seminario Matematico della Università di Padova

On compactness and connectedness of the paratingent

Wojciech Zygmunt — 2016

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

In this note we shall prove that for a continuous function $ϕ : Δ \to ℝ^{n}$ , where $Δ \subset ℝ$ , the paratingent of $ϕ$ at $a \in Δ$ is a non-empty and compact set in $ℝ^{n}$ if and only if $ϕ$ satisfies Lipschitz condition in a neighbourhood of $a$ . Moreover, in this case the paratingent is a connected set.

On superpositionally measurable semi-Carathéodory multifunctions

Wojciech Zygmunt — 1992

Commentationes Mathematicae Universitatis Carolinae

For multifunctions $F : T \times X \to 2^{Y}$ , measurable in the first variable and semicontinuous in the second one, a relation is established between being product measurable and being superpositionally measurable.

On superpositional measurability of semi-Carathéodory multifunctions

Wojciech Zygmunt — 1994

Commentationes Mathematicae Universitatis Carolinae

It is shown that product weakly measurable lower weak semi-Carathéodory multifunction is superpositionally measurable.

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