Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
variation; oscillation; modulus of variation; selection theorem
variation; oscillation; modulus of variation; selection theorem
Summary:
We compare a recent selection theorem given by Chistyakov using the notion of modulus of variation, with a selection theorem of Schrader based on bounded oscillation and with a selection theorem of Di Piazza-Maniscalco based on bounded ${\mathcal A},\Lambda $-oscillation.
References:
[1] Bongiorno B., Vetro P.: Su un teorema di F. Riesz. Atti Acc. Sc. Lett. Arti Palermo, Ser. IV 37 (1977–78), 3–13. MR 0624502
[2] Chanturiya Z. A.: The modulus of variation of a function and its application in the theory of Fourier series. Soviet. Math. Dokl. 15 (1974), 67–71. Zbl 0295.26008
[3] Chistyakov V. V.: A selection principle for functions of a real variable. Atti Sem. Mat. Fis. Univ. Modena e Reggio Emilia 53 (2005), 25–43. MR 2199030 | Zbl 1115.26006
[4] Chistyakov V. V.: The optimal form of selection principle for functions of a real variable. J. Math. Anal. Appl. 310 (2005), 609–625. DOI 10.1016/j.jmaa.2005.02.028 | MR 2022947
[5] Di Piazza L., Maniscalco C.: Selection theorems, based on generalized variation and oscillation. Rend. Circ. Mat. Palermo, Ser. II 35 (1986), 386–396. DOI 10.1007/BF02843906 | MR 0929621
[6] Helly E.: Über linear Funktionaloperationen. Sitzungsber. Naturwiss. Kl. Kaiserlichen Akad. Wiss. Wien 121 (1912), 265–297.
[7] Henstock H.: The General Theory of Integration. Clarendon Press, Oxford, U.K., 1991. MR 1134656 | Zbl 0745.26006
[8] Musielak J., Orlicz W.: On generalized variations (I). Studia Math. 18 (1959), 11–41. DOI 10.4064/sm-18-1-11-41 | MR 0104771
[9] Schrader K.: A generalization of the Helly selection theorem. Bull. Amer. Math. Soc. 78 (1972), 415–419. DOI 10.1090/S0002-9904-1972-12923-9 | MR 0299740 | Zbl 0236.40001
[10] Waterman D.: On $\Lambda $-bounded variation. Studia Math. 57 (1976), 33–45. DOI 10.4064/sm-57-1-33-45 | MR 0417355 | Zbl 0341.26008
Search
Partner of
