Pointwise measurable functions

Authors

  • Herman Render
  • Lothar Rogge

DOI:

https://doi.org/10.7146/math.scand.a-14462

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 $\sigma$-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.

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Published

2004-12-01

How to Cite

Render, H., & Rogge, L. (2004). Pointwise measurable functions. MATHEMATICA SCANDINAVICA, 95(2), 305–319. https://doi.org/10.7146/math.scand.a-14462

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Section

Articles