Geodesic
A PU-integral on an abstract metric space
Mathematica Bohemica, Tome 122 (1997) no. 1, pp. 83-95

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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.
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.
DOI : 10.21136/MB.1997.126181
Classification : 26A39, 28A25, 46G12
Keywords: PU-integral; partition of unity 
Riccobono, Giuseppa. A PU-integral on an abstract metric space. Mathematica Bohemica, Tome 122 (1997) no. 1, pp. 83-95. doi: 10.21136/MB.1997.126181
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