Convergence theorems for the PU-integral
We give a definition of uniform PU-integrability for a sequence of -measurable real functions defined on an abstract metric space and prove that it is not equivalent to the uniform -integrability.
A PU-integral on an abstract metric space
In this paper, we define a -integral, i.e. an integral defined by means of partitions of unity, on a suitable compact metric measure space, whose measure is compatible with its topology in the sense that every open set is -measurable. We prove that the -integral is equivalent to -integral. Moreover, we give an example of a noneuclidean compact metric space such that the above results are true.
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