| Title:
|
Logarithmic capacity is not subadditive – a fine topology approach (English) |
| Author:
|
Pyrih, Pavel |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
1 |
| Year:
|
1992 |
| Pages:
|
67-72 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In Landkof's monograph [8, p. 213] it is asserted that logarithmic capacity is strongly subadditive, and therefore that it is a Choquet capacity. An example demonstrating that logarithmic capacity is not even subadditive can be found e.g\. in [6, Example 7.20], see also [3, p. 803]. In this paper we will show this fact with the help of the fine topology in potential theory. (English) |
| Keyword:
|
logarithmic capacity |
| Keyword:
|
fine topology |
| MSC:
|
30C85 |
| MSC:
|
31A15 |
| MSC:
|
31C40 |
| MSC:
|
60J45 |
| idZBL:
|
Zbl 0764.31006 |
| idMR:
|
MR1173748 |
| . |
| Date available:
|
2009-01-08T17:53:38Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118472 |
| . |
| Reference:
|
[1] Brelot M.: Lectures on Potential Theory.Tata Institute of Fundamental Research Bombay (1966). MR 0118980 |
| Reference:
|
[2] Brelot M.: On Topologies and Boundaries in Potential Theory.Lecture Notes in Mathematics No. 175, Springer-Verlag, Berlin (1971). Zbl 0222.31014, MR 0281940 |
| Reference:
|
[3] Doob J.L.: Classical Potential Theory and Its Probabilistic Counterpart.Springer, New-York (1984). Zbl 0549.31001, MR 0731258 |
| Reference:
|
[4] Fuglede B.: Fine Topology and Finely Holomorphic Functions.Proc. 18th Scand. Congr. Math. Aarhus (1980), 22-38. MR 0633349 |
| Reference:
|
[5] Fuglede B.: Sur les fonctions finement holomorphes.Ann. Inst. Fourier (Grenoble) 31.4 (1981), 57-88. Zbl 0445.30040, MR 0644343 |
| Reference:
|
[6] Hayman W.K.: Subharmonic functions, Vol.2.London Math. Society Monographs 20, Academic Press London (1989). MR 1049148 |
| Reference:
|
[7] Helms L.L.: Introduction to Potential Theory.Wiley Interscience Pure and Applied Mathematics 22, New-York (1969). Zbl 0188.17203, MR 0261018 |
| Reference:
|
[8] Landkof N.S.: Foundations of Modern Potential Theory.Russian Moscow (1966). |
| Reference:
|
[9] Landkof N.S.: Foundations of Modern Potential Theory.(translation from [8]), Springer-Verlag, Berlin (1972). Zbl 0253.31001, MR 0350027 |
| Reference:
|
[10] Lukeš J., Malý J., Zajíček L.: Fine Topology Methods in Real Analysis and Potential Theory.Lecture Notes in Mathematics No. 1189, Springer-Verlag, Berlin (1986). MR 0861411 |
| . |
