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Abstract and Applied Analysis
Volume 2011, Article ID 582576, 7 pages
http://dx.doi.org/10.1155/2011/582576
Research Article

On 𝑝-Convergence in Measure of a Sequence of Measurable Functions

1Department of Mathematics and Computer Sciences, University of Perugia, Via Vanvitelli 1, 06123 Perugia, Italy
2Department of Mathematics, University of Athens, Panepistimiopolis, 15784 Athens, Greece

Received 18 November 2010; Accepted 22 March 2011

Academic Editor: Agacik Zafer

Copyright © 2011 A. Boccuto et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Boccuto and D. Candeloro, β€œIntegral and ideals in Riesz spaces,” Information Sciences, vol. 179, no. 17, pp. 2891–2902, 2009. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  2. J. Haluška, β€œOn integration in complete vector lattices,” Tatra Mountains Mathematical Publications, vol. 3, pp. 201–212, 1993. View at Google Scholar Β· View at Zentralblatt MATH
  3. J. Haluška and O. Hutník, β€œOn convergences of measurable functions in Archimedean vector lattices,” Positivity, vol. 14, no. 3, pp. 515–527, 2010. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  4. I. Dobrakov and T. V. Panchapagesan, β€œA generalized Pettis measurability criterion and integration of vector functions,” Studia Mathematica, vol. 164, no. 3, pp. 205–229, 2004. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  5. T. V. Panchapagesan, The Bartle-Dunford-Schwartz Integral. Integration with Respect to a Sigma-Additive Vector Measure, vol. 69 of Mathematics Institute of the Polish Academy of Sciences. Mathematical Monographs (New Series), Birkhäuser, Basel, Switzerland, 2008.
  6. A. Boccuto, B. Riečan, and M. Vrábelová, Kurzweil-Henstock Integral in Riesz Spaces, Bentham Science, 2009.
  7. B. Riečan and T. Neubrunn, Integral, Measure, and Ordering, vol. 411 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997.
  8. B. Riečan and M. Vrábelová, β€œThe Kurzweil construction of an integral in ordered spaces,” Czechoslovak Mathematical Journal, vol. 48(123), no. 3, pp. 565–574, 1998. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  9. H. Kunita, β€œItô's stochastic calculus: its surprising power for applications,” Stochastic Processes and their Applications, vol. 120, no. 5, pp. 622–652, 2010. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  10. N. Papanastassiou and C. Papachristodoulos, β€œp-convergence in measure of a sequence of measurable functions and corresponding minimal elements of c0,” Positivity, vol. 13, no. 1, pp. 243–253, 2009. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  11. N. Dunford and J. T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, New York, NY, USA, 1958.