Equivanishing sequences of mappings

Piotr Antosik

Banach Center Publications (2000)

  • Volume: 53, Issue: 1, page 89-104
  • ISSN: 0137-6934

Abstract

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Utilizing elementary properties of convergence of numerical sequences we prove Nikodym, Banach, Orlicz-Pettis type theorems

How to cite

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Antosik, 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

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  1. [1] P. Antosik, On the Mikusiński diagonal theorem, Bull. Acad. Polon. Sci. 19 (1971), 305-310. Zbl0211.42703
  2. [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. [3] P. Antosik, A lemma on matrices and its applications, Contemporary Math. 52 (1986), 89-95. 
  4. [4] P. Antosik, J. Mikusiński and R. Sikorski, Theory of Distributions. Sequential Approach, Elsevier, Amsterdam, 1973. Zbl0267.46028
  5. [5] P. Antosik and C. Schwartz, Matrix methods in analysis, Lecture Notes in Math. 1119, Springer, Heidelberg, 1985. 
  6. [6] S. Banach, Théorie des opérations linéaires, Monografie Mat., vol. 1, Warszawa, 1932. Zbl0005.20901
  7. [7] J. Distel, Sequences and series in Banach spaces, Springer Verlag, 1984. 
  8. [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. [9] L. Drewnowski, Equivalence of Brooks-Jewett, Vitali-Hahn-Saks and Nikodym Theorems, Bull. Acad. Polon. Sci. 20 (1972), 725-731. Zbl0243.28011
  10. [10] N. J. Kalton, Subseries convergence in topological groups and vector spaces, Israel J. Math. 10 (1971), 402-412. Zbl0226.22005
  11. [11] C. Kliś, An example of a non-complete normed K-space, Bull. Acad. Polon. Sci. 26 (1978), 415-420. Zbl0393.46017
  12. [12] G. Köthe, Topological vector spaces I, Springer Verlag, Berlin 1969. Zbl0179.17001
  13. [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. [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. [15] J. Mikusiński, Aksjomatyczna teoria zbieżności, preprint. 
  16. [16] O. M. Nikodym, Sur les familles bornées de fonctions parfaitement additives d'ensembles abstraits, Monatsh. Math. Phys., 1933, 40. Zbl59.0270.02
  17. [17] W. Orlicz, Beiträge zur Theorie der Orthogonalentwicklungen II, Studia Math. 1 (1929), 241-255. Zbl55.0164.02
  18. [18] B. J. Pettis, Integration in vector spaces, Trans. Amer. Math. Soc., 44, 277-304. Zbl0019.41603
  19. [19] C. Schwartz, Infinite matrices and the gliding hump, World Scientific, 1996. Zbl0923.46003
  20. [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. [21] A. Vilensky, Modern methods in topological vector spaces, McGraw-Hill, N.Y., 1978. 

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