Equivanishing sequences of mappings
Banach Center Publications (2000)
- Volume: 53, Issue: 1, page 89-104
- ISSN: 0137-6934
Access Full Article
topAbstract
topHow to cite
topAntosik, Piotr. "Equivanishing sequences of mappings." Banach Center Publications 53.1 (2000): 89-104. <http://eudml.org/doc/209080>.
@article{Antosik2000,
abstract = {Utilizing elementary properties of convergence of numerical sequences we prove Nikodym, Banach, Orlicz-Pettis type theorems},
author = {Antosik, Piotr},
journal = {Banach Center Publications},
keywords = {uniform strong additivity; equicontinuity; subseries convergent series; uniformlly equivanishing sequence; uniformly countable additivity},
language = {eng},
number = {1},
pages = {89-104},
title = {Equivanishing sequences of mappings},
url = {http://eudml.org/doc/209080},
volume = {53},
year = {2000},
}
TY - JOUR
AU - Antosik, Piotr
TI - Equivanishing sequences of mappings
JO - Banach Center Publications
PY - 2000
VL - 53
IS - 1
SP - 89
EP - 104
AB - Utilizing elementary properties of convergence of numerical sequences we prove Nikodym, Banach, Orlicz-Pettis type theorems
LA - eng
KW - uniform strong additivity; equicontinuity; subseries convergent series; uniformlly equivanishing sequence; uniformly countable additivity
UR - http://eudml.org/doc/209080
ER -
References
top- [1] P. Antosik, On the Mikusiński diagonal theorem, Bull. Acad. Polon. Sci. 19 (1971), 305-310. Zbl0211.42703
- [2] P. Antosik, A diagonal theorem for nonnegative metrices and equicontinuous sequences of mappings, Bull. Acad. Polon. Sci. 24 (1976), 855-859. Zbl0342.40004
- [3] P. Antosik, A lemma on matrices and its applications, Contemporary Math. 52 (1986), 89-95.
- [4] P. Antosik, J. Mikusiński and R. Sikorski, Theory of Distributions. Sequential Approach, Elsevier, Amsterdam, 1973. Zbl0267.46028
- [5] P. Antosik and C. Schwartz, Matrix methods in analysis, Lecture Notes in Math. 1119, Springer, Heidelberg, 1985.
- [6] S. Banach, Théorie des opérations linéaires, Monografie Mat., vol. 1, Warszawa, 1932. Zbl0005.20901
- [7] J. Distel, Sequences and series in Banach spaces, Springer Verlag, 1984.
- [8] V. M. Doubrovsky (Dubrovskii), On some properties of complete set functions and their application to a generalization of a theorem of Lebesgue, Mat. Sb. 20 (62) (1947), 317-329.
- [9] L. Drewnowski, Equivalence of Brooks-Jewett, Vitali-Hahn-Saks and Nikodym Theorems, Bull. Acad. Polon. Sci. 20 (1972), 725-731. Zbl0243.28011
- [10] N. J. Kalton, Subseries convergence in topological groups and vector spaces, Israel J. Math. 10 (1971), 402-412. Zbl0226.22005
- [11] C. Kliś, An example of a non-complete normed K-space, Bull. Acad. Polon. Sci. 26 (1978), 415-420. Zbl0393.46017
- [12] G. Köthe, Topological vector spaces I, Springer Verlag, Berlin 1969. Zbl0179.17001
- [13] I. Labuda and Z. Lipecki, On subseries convergent series and m-quasi-bases in topological spaces, Manuscr. Math. 38 (1981), 87-98. Zbl0496.46006
- [14] J. Mikusiński, A theorem on vector matrices and its application in measure theory and functional analysis, Bull. Polon. Acad. Sci. 18 (1970), 193-196.
- [15] J. Mikusiński, Aksjomatyczna teoria zbieżności, preprint.
- [16] O. M. Nikodym, Sur les familles bornées de fonctions parfaitement additives d'ensembles abstraits, Monatsh. Math. Phys., 1933, 40. Zbl59.0270.02
- [17] W. Orlicz, Beiträge zur Theorie der Orthogonalentwicklungen II, Studia Math. 1 (1929), 241-255. Zbl55.0164.02
- [18] B. J. Pettis, Integration in vector spaces, Trans. Amer. Math. Soc., 44, 277-304. Zbl0019.41603
- [19] C. Schwartz, Infinite matrices and the gliding hump, World Scientific, 1996. Zbl0923.46003
- [20] H. Weber, Compactness in spaces of group valued contents, the Vitali-Hahn-Saks theorem and Nikodym boundedness theorem, Rocky Mt. J. Math. 16 (1986), 253-275. Zbl0604.28006
- [21] A. Vilensky, Modern methods in topological vector spaces, McGraw-Hill, N.Y., 1978.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.