| Title:
|
Variations of additive functions (English) |
| Author:
|
Buczolich, Zoltán |
| Author:
|
Pfeffer, Washek F. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
47 |
| Issue:
|
3 |
| Year:
|
1997 |
| Pages:
|
525-555 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the relationship between derivates and variational measures of additive functions defined on families of figures or bounded sets of finite perimeter. Our results, valid in all dimensions, include a generalization of Ward’s theorem, a necessary and sufficient condition for derivability, and full descriptive definitions of certain conditionally convergent integrals. (English) |
| MSC:
|
26B05 |
| MSC:
|
26B30 |
| MSC:
|
28A75 |
| MSC:
|
49Q15 |
| MSC:
|
58C35 |
| idZBL:
|
Zbl 0903.26004 |
| idMR:
|
MR1461431 |
| . |
| Date available:
|
2009-09-24T10:08:10Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127376 |
| . |
| Reference:
|
[B] B. Bongiorno: Essential variation.Measure Theory Oberwolfach 1981, Springer Lecture Notes Math., 945, 1981, pp. 187–193. MR 0675282 |
| Reference:
|
[BPS] B. Bongiorno, L. Di Piazza and V. Skvortsov: The essential variation of a function and some convergence theorems.Anal. Math. 22 (1996), no. 1, 3–12. MR 1384345, 10.1007/BF02342334 |
| Reference:
|
[BPT] B. Bongiorno, W.F. Pfeffer and B.S. Thomson: A full descriptive definition of the gage integral.Canadian Math. Bull. 39 (1996), no. 4, 390–401. MR 1426684, 10.4153/CMB-1996-047-x |
| Reference:
|
[BV] B. Bongiorno and P. Vetro: Su un teorema di F. Riesz.Atti Acc. Sci. Lettere e Arti Palermo (IV) 37 (1979), 3–13. |
| Reference:
|
[Di] L. Di Piazza: A note on additive functions of intervals.Real Anal. Ex. 20(2) (1994–95), 815–818. MR 1348103 |
| Reference:
|
[EG] L.C. Evans and R.F. Gariepy: Measure Theory and Fine Properties of Functions.CRC Press, Boca Raton, 1992. MR 1158660 |
| Reference:
|
[Fe] H. Federer: Geometric Measure Theory.Springer-Verlag, New York, 1969. Zbl 0176.00801, MR 0257325 |
| Reference:
|
[Gu] E. Giusti: Minimal Surfaces and Functions of Bounded Variation.Birkhäuser, Basel, 1984. Zbl 0545.49018, MR 0775682 |
| Reference:
|
[P1] W.F. Pfeffer: The Gauss-Green theorem.Adv. Math. 87 (1991), 93–147. Zbl 0732.26013, MR 1102966, 10.1016/0001-8708(91)90063-D |
| Reference:
|
[P3] W.F. Pfeffer: A descriptive definition of a variational integral and applications.Indiana Univ. Math. J. 40 (1991), 259–270. Zbl 0747.26010, MR 1101229, 10.1512/iumj.1991.40.40011 |
| Reference:
|
[P] W.F. Pfeffer: The Riemann Approach to Integration.Cambridge Univ. Press, Cambridge, 1993. Zbl 0804.26005, MR 1268404 |
| Reference:
|
[Sa] S. Saks: Theory of the Integral.Dover, New York, 1964. MR 0167578 |
| Reference:
|
[St] E.M. Stein: Singular Integrals and Differentiability Properties of Function.Princeton Univ. Press, Princeton, 1970. MR 0290095 |
| Reference:
|
[T] B. S. Thomson: Derivates of Interval Functions.Mem. Amer. Math. Soc., #452, Providence, 1991. Zbl 0734.26003, MR 1078198 |
| Reference:
|
[V] A.I. Volpert: The spaces $BV$ and quasilinear equations.Math. USSR-SB. 2 (1967), 255–267. MR 0216338 |
| . |
