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Keywords:
PU-integral; partition of unity
Summary:
In this paper, we define a $\PU$-integral, i.e. an integral defined by means of partitions of unity, on a suitable compact metric measure space, whose measure $\mu$ is compatible with its topology in the sense that every open set is $\mu$-measurable. We prove that the $\PU$-integral is equivalent to $\mu$-integral. Moreover, we give an example of a noneuclidean compact metric space such that the above results are true.
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