MATHEMATICA BOHEMICA, Vol. 122, No. 1, pp. 83-95 (1997)

A $\mathop PU$-integral on an abstract metric space

Giuseppa Riccobono

Giuseppa Riccobono, Dipartimento di Matematica ed Applicazioni, Universita di Palermo, Via Archirafi 34, 90123 Palermo, Italy, e-mail:

Abstract: 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.

Keywords: PU-integral, partition of unity

Classification (MSC2000): 28A25

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