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Ewert, J.

On measurability of quasi-continuous and some related maps. (English) Zbl 0649.54005

Period. Math. Hung. 20, No. 4, 299-304 (1989).
Let X, Y be topological spaces, \({\mathcal A}\) any family of maps from X into Y. \({\mathcal S}({\mathcal A})\) denotes the smallest \(\sigma\)-algebra of subsets of X with respect to which all maps belonging to \({\mathcal A}\) are measurable. If X is a perfectly normal space, Y is a \(T_ 1\)-space with at least two points and \({\mathcal A}\) consists of all quasi-continuous maps [S. Kempisty, Fundam. Math. 19, 184-197 (1932; Zbl 0005.19802)] (resp. irresolute maps [S. G. Crossley and S. K. Hildebrand, Fundam. Math. 74, 233-254 (1972; Zbl 0206.515)]) then \({\mathcal S}({\mathcal A})\) coincides with the \(\sigma\)-algebra of sets with the Baire property.
For upper and lower measurability of multivalued maps analogous theorems are true.
Reviewer: J.Ewert

MSC:

54C60 Set-valued maps in general topology
54C08 Weak and generalized continuity
28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence

Citations:

Zbl 0005.19802; Zbl 0206.515
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\textit{J. Ewert}, Period. Math. Hung. 20, No. 4, 299--304 (1989; Zbl 0649.54005)
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References:

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