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Given a coarse space with the bornology of bounded subsets, we extend the coarse structure from to the natural coarse structure on and say that a macro-uniform mapping (or ) is a selector (or 2-selector) of if for each (, respectively). We prove that a discrete coarse space admits a selector if and only if admits a 2-selector if and only if there exists a linear order “" on such that the family of intervals is a base for the bornology .
Let . For n ≥ 2, we prove that if Selivanovski measurable functions from to Z give as preimages of H all Σₙ¹ subsets of , then so do continuous injections.
Let Ω be a measure space, and E, F be separable Banach spaces. Given a multifunction , denote by the set of all measurable selections of the multifunction , s ↦ f(s,x(s)), for a function x: Ω → E. First, we obtain new theorems on H-upper/H-lower/lower semicontinuity (without assuming any conditions on the growth of the generating multifunction f(s,u) with respect to u) for the multivalued (Nemytskiĭ) superposition operator mapping some open domain G ⊂ X into , where X and Y are Köthe-Bochner...
Viene studiata la semicontinuità rispetto alla topologia di per alcuni funzionali del Calcolo delle Variazioni dipendenti da funzioni a valori vettoriali.
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