A PU-integral on an abstract metric space

Giuseppa Riccobono

Mathematica Bohemica (1997)

  • Volume: 122, Issue: 1, page 83-95
  • ISSN: 0862-7959

Abstract

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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 μ is compatible with its topology in the sense that every open set is μ -measurable. We prove that the -integral is equivalent to μ -integral. Moreover, we give an example of a noneuclidean compact metric space such that the above results are true.

How to cite

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Riccobono, Giuseppa. "A PU-integral on an abstract metric space." Mathematica Bohemica 122.1 (1997): 83-95. <http://eudml.org/doc/248118>.

@article{Riccobono1997,
abstract = {In this paper, we define a $$-integral, i.e. an integral defined by means of partitions of unity, on a suitable compact metric measure space, whose measure $\mu $ is compatible with its topology in the sense that every open set is $\mu $-measurable. We prove that the $$-integral is equivalent to $\mu $-integral. Moreover, we give an example of a noneuclidean compact metric space such that the above results are true.},
author = {Riccobono, Giuseppa},
journal = {Mathematica Bohemica},
keywords = {PU-integral; partition of unity; PU-integral; partition of unity},
language = {eng},
number = {1},
pages = {83-95},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A PU-integral on an abstract metric space},
url = {http://eudml.org/doc/248118},
volume = {122},
year = {1997},
}

TY - JOUR
AU - Riccobono, Giuseppa
TI - A PU-integral on an abstract metric space
JO - Mathematica Bohemica
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 122
IS - 1
SP - 83
EP - 95
AB - In this paper, we define a $$-integral, i.e. an integral defined by means of partitions of unity, on a suitable compact metric measure space, whose measure $\mu $ is compatible with its topology in the sense that every open set is $\mu $-measurable. We prove that the $$-integral is equivalent to $\mu $-integral. Moreover, we give an example of a noneuclidean compact metric space such that the above results are true.
LA - eng
KW - PU-integral; partition of unity; PU-integral; partition of unity
UR - http://eudml.org/doc/248118
ER -

References

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  2. D. Caponetti, V. Marraffa, An integral in the real line defined by BV partitions of unity, Atti Semin. Mat. Fis., Univ. Modena, 42 (1994), 69-82. (1994) Zbl0824.26004MR1282323
  3. R. O. Davies, Z. Schuss, 10.1112/jlms/2.Part_3.561, J. London Math. Soc. (2) 2 (1970), 561-562. (1970) Zbl0197.04103MR0265526DOI10.1112/jlms/2.Part_3.561
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  9. J. Jarník, J. Kurzweil, A new and more powerful concept of the PU-integral, Czechoslovak Math. J. 38 (113) (1988), 8-48. (1988) MR0925939
  10. J. Kurzweil J. Mawhin, W. Pfeffer, An integral defined by approximating BV paгtitions of unity, Czechoslovak Math. J. 41 (116) (1991), 695-712. (1991) MR1134958
  11. W. F. Pfeffer, 10.1090/S0002-9947-1986-0833702-0, Trans. Amer. Math. Soc. 295 (2) (1986), 665-685. (1986) Zbl0596.26007MR0833702DOI10.1090/S0002-9947-1986-0833702-0
  12. W. F. Pfeffer, Wei-Chi Yang, A note on conditionally convergent integrals, Real Anal. Exchange 17 (1991/92), 815-819. (1991) MR1171426
  13. W. F. Pfeffer, The Riemann approach to integration, Cambridge University Pгess, 1993. (1993) Zbl0804.26005MR1268404

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