| Title:
|
A comparison of three recent selection theorems (English) |
| Author:
|
Maniscalco, Caterina |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
132 |
| Issue:
|
2 |
| Year:
|
2007 |
| Pages:
|
177-183 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
variation |
| Keyword:
|
oscillation |
| Keyword:
|
modulus of variation |
| Keyword:
|
selection theorem |
| MSC:
|
26A45 |
| MSC:
|
40A30 |
| idZBL:
|
Zbl 1174.26311 |
| idMR:
|
MR2338804 |
| DOI:
|
10.21136/MB.2007.134188 |
| . |
| Date available:
|
2009-09-24T22:30:34Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134188 |
| . |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[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. Zbl 1115.26006, MR 2199030 |
| Reference:
|
[4] Chistyakov V. V.: The optimal form of selection principle for functions of a real variable.J. Math. Anal. Appl. 310 (2005), 609–625. MR 2022947, 10.1016/j.jmaa.2005.02.028 |
| Reference:
|
[5] Di Piazza L., Maniscalco C.: Selection theorems, based on generalized variation and oscillation.Rend. Circ. Mat. Palermo, Ser. II 35 (1986), 386–396. MR 0929621, 10.1007/BF02843906 |
| Reference:
|
[6] Helly E.: Über linear Funktionaloperationen.Sitzungsber. Naturwiss. Kl. Kaiserlichen Akad. Wiss. Wien 121 (1912), 265–297. |
| Reference:
|
[7] Henstock H.: The General Theory of Integration.Clarendon Press, Oxford, U.K., 1991. Zbl 0745.26006, MR 1134656 |
| Reference:
|
[8] Musielak J., Orlicz W.: On generalized variations (I).Studia Math. 18 (1959), 11–41. MR 0104771, 10.4064/sm-18-1-11-41 |
| Reference:
|
[9] Schrader K.: A generalization of the Helly selection theorem.Bull. Amer. Math. Soc. 78 (1972), 415–419. Zbl 0236.40001, MR 0299740, 10.1090/S0002-9904-1972-12923-9 |
| Reference:
|
[10] Waterman D.: On $\Lambda $-bounded variation.Studia Math. 57 (1976), 33–45. Zbl 0341.26008, MR 0417355, 10.4064/sm-57-1-33-45 |
| . |
