Abstract: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 σ -compact metric space, then this set is a G δ -set; if the range space is only a Polish space this is in gen… Show more
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