Pointwise measurable functions
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We introduce the new concept of pointwise measurability. It is shown in this paper that a measurable function is measurable at each point and that for a large class of topological spaces the converse also holds. Moreover it can be seen that a function which is continuous at a point is Borel-measurable at this point too. Furthermore the set of measurability points is considered. If the range space is a $\sigma$-compact metric space, then this set is a $G_{\delta}$-set; if the range space is only a Polish space this is in general not true any longer.
1966 ◽
Vol 18
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pp. 1264-1271
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1999 ◽
Vol 19
(4)
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pp. 1063-1076
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1993 ◽
Vol 16
(2)
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pp. 259-266
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1978 ◽
Vol 30
(01)
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pp. 32-44
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