Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Cover of the book
Tytuł książki

Relativization of some aspects of the theory of functions of bounded variation

Seria
Rozprawy Matematyczne tom/nr w serii: 320 wydano: 1992
Zawartość
Warianty tytułu
Abstrakty
EN

CONTENTS
I. Introduction and preliminaries.....................................5
II. Mutual singularities...................................................14
III. Relative absolute continuities...................................33
IV. Normalized relative derivative..................................50
V. Relativization of other classical theorems.................73
VI. Convergence in B....................................................95
References.................................................................119
Index of symbols.........................................................121
Index of terms.............................................................123
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 320
Liczba stron
123
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCXX
Daty
wydano
1992
otrzymano
1990-10-05
poprawiono
1991-09-20
Twórcy
  • Department of Mathematics, Faculty of Science, University of Alberta, Edmonton, Alberta Canada T6G 2G1
Bibliografia
  • [1] P. S. Bullen, Non-absolute integrals: a survey, Real Anal. Exchange 5 (1979-80), 195-259.
  • [2] M. C. Chakrabarty, Some results on AC-ω functions, Fund. Math. 64 (1969), 219-230.
  • [3] G. Choquet, Topology, Academic Press, New York 1966.
  • [4] P. J. Daniell, Differentiation with respect to a function of limited variation, Trans. Amer. Math. Soc. 19 (1918), 353-362.
  • [5] Ch. J. de La Vallée Poussin, Sur l'intégrale de Lebesgue, Trans. Amer. Math. Soc. 16 (1915), 435-501.
  • [6] Ch. J. de La Vallée Poussin, Intégrales de Lebesgue, Fonctions d'ensemble, Classes de Baire, 2e éd., Gauthier-Villars, Paris 1950.
  • [7] A. Denjoy, L'additivité métrique vectorielle des ensembles et les discontinuités tangentielles sur les courbes rectifiables, Bull. Math. Soc. Roumaine Sci. 35 (1933), 83-105.
  • [8] N. Dunford and J. T. Schwartz, Linear Operators, Part I, Interscience, New York 1964.
  • [9] G. Fubini, Sulla derivazione per serie, Atti Accad. Naz. Lincei Rend. 24 (1915), 204-206.
  • [10] K. M. Garg, On nowhere monotone functions, Thesis, Lucknow University, Lucknow (India), 1962.
  • [11] K. M. Garg, On singular functions, Rev. Roumaine Math. Pures Appl. 14 (1969), 1441-1452.
  • [12] K. M. Garg, Characterizations of absolutely continuous and singular functions, in: Proc. of Conference on Constructive Theory of Functions (Approximation Theory) (Budapest 1969), Akadémiai Kiadó, Budapest 1972, 183-188.
  • [13] K. M. Garg, On bilateral derivates and the derivative, Trans. Amer. Math. Soc. 210 (1975), 295-329.
  • [14] K. M. Garg, Construction of absolutely continuous and singular functions that are nowhere of monotonic type, in: Contemp. Math. 42, Amer. Math. Soc., Providence, R.I., 1985, 61-79.
  • [15] K. M. Garg, Decompositions of mutual singularity and relative absolute continuity of signed measures , to appear.
  • [16] K. M. Garg, Properties of typical functions in some subspaces of the space of functions of bounded variation, to appear.
  • [17] P. R. Halmos, Measure Theory, Van Nostrand, New York 1950.
  • [18] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. I, Springer, New York 1963.
  • [19] E. Hewitt and K. Stromberg, Real and Abstract Analysis, Springer, New York 1965.
  • [20] E. W. Hobson, The Theory of Functions of a Real Variable and the Theory of Fourier's Series, Vol. II, Dover, New York 1958.
  • [21] R. L. Jeffery, Non-absolutely convergent integrals with respect to functions of bounded variation, Trans. Amer. Math. Soc. 34 (1932), 645-675.
  • [22] R. L. Jeffery, Generalized integrals with respect to functions of bounded variation, Canad. J. Math. 10 (1958), 617-626.
  • [23] H. Kober, On decompositions and transformations of functions of bounded variation, Ann. of Math. 53 (1951), 565-580.
  • [24] K. Kuratowski, Topology, Vol. I, Academic Press, New York 1966.
  • [25] K. Kuratowski, Topology, Vol. II, Academic Press, New York 1968.
  • [26] H. Lebesgue, Leçons sur l'intégration et la recherche des fonctions primitives, 3rd ed., Chelsea, New York 1973.
  • [27] N. Lusin, Integral and Trigonometric Series, Moscow 1915 (in Russian).
  • [28] I. P. Natanson, Theory of Functions of a Real Variable, Vol. I, Ungar, New York 1955.
  • [29] I. P. Natanson, Theory of Functions of a Real Variable, Vol. II, Ungar, New York 1960.
  • [30] H. Rademacher, Eineindeutige Abbildungen und Messbarkeit, Monatsh. Math. Phys. 27 (1916), 183-291.
  • [31] J. Radon, Theorie und Anwendungen der absolut additiven Mengenfunktionen, S.B. Akad. Wiss. Wien 122 (1913), 1295-1438.
  • [32] J. Ridder, Über den Perronschen Integralbegriff und seine Beziehung zu den R-, L- und D-Integralen, Math. Z. 34 (1931), 234-269.
  • [33] H. L. Royden, Real Analysis, 2nd ed., Macmillan, New York 1968.
  • [34] S. Saks, Theory of the Integral, Monografie Mat. 7, PWN, Warszawa 1937.
  • [35] L. Tonelli, Sulla rettificazione delle curve, Atti Accad. Sci. Torino 43 (1908), 399-416.
  • [36] L. Tonelli, Sul differenziale dell'arco di curva, Atti Accad. Naz. Lincei (5) 25 (1) (1916), 207-213.
  • [37] W. H. Young, On integrals and derivates with respect to a function, Proc. London Math. Soc. 15 (1917), 35-63.
  • [38] Z. Zahorski, Sur l'ensemble des points de non-dérivabilité d'une fonction continue, Bull. Soc. Math. France 74 (1946), 147-178.
Języki publikacji
EN
Uwagi
1991Mathematics Subject Classification:Primary 26-02, 26A42, 26A45, 28-02; Secondary 26A15, 26A24, 26A30, 26A46, 28A75
Identyfikator YADDA
bwmeta1.element.dl-catalog-01a74bc4-d4a1-4aaa-a558-22f47fa5540c
Identyfikatory
ISBN
83-85116-48-6
ISSN
0012-3862
Kolekcja
DML-PL
Zawartość książki

rozwiń roczniki

JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.