Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A Volterra type derivative of the Lebesgue integral


Author: Washek F. Pfeffer
Journal: Proc. Amer. Math. Soc. 117 (1993), 411-416
MSC: Primary 28A15; Secondary 46G12
DOI: https://doi.org/10.1090/S0002-9939-1993-1135079-1
MathSciNet review: 1135079
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Using functions of bounded variation, we define a Volterra type derivative of the linear functional associated with a Lebesgue integrable function and show that it is equal to this function almost everywhere.


References [Enhancements On Off] (What's this?)

  • [HN] E. P. Hamilton and M. Z. Nashed, Global and local variational derivatives and integral representations of Gâteaux differentials, J. Funct. Anal. 49 (1982), 128-144. MR 680859 (84i:58017)
  • [G] E. Giusti, Minimal surfaces and functions of bounded variation, Birkhäuser, Basel, 1984. MR 775682 (87a:58041)
  • [KMP] J. Kurzweil, J. Mawhin, and W. F. Pfeffer, An integral defined by approximating $ BV$ partitions of unity, Czechoslovak Math. J. (to appear). MR 1134958 (92k:26026)
  • [P1] W. F. Pfeffer, On the continuity of the Volterra variational derivative, J. Funct. Anal. 71 (1987), 195-197. MR 879708 (88i:46058)
  • [R] W. Rudin, Real and complex analysis, McGraw-Hill, New York, 1987. MR 924157 (88k:00002)
  • [S] S. Saks, Theory of the integral, Dover, New York, 1964. MR 0167578 (29:4850)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28A15, 46G12

Retrieve articles in all journals with MSC: 28A15, 46G12


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1135079-1
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society