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Zawartość
Pełne teksty:
![http://matwbn.icm.edu.pl/ksiazki/rm/rm320/rm32001.pdf [zdalny]](images/mime-icons/pdf.gif "Tom CCCXX")
Warianty tytułu
Abstrakty
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
Słowa kluczowe
Tematy
Kategoryzacja MSC:
- 26-02: Research exposition (monographs, survey articles)
- 26A46: Absolutely continuous functions
- 28A75: Length, area, volume, other geometric measure theory
- 26A45: Functions of bounded variation, generalizations
- 28-02: Research exposition (monographs, survey articles)
- 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems
- 26A42: Integrals of Riemann, Stieltjes and Lebesgue type
- 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.)
- 26A30: Singular functions, Cantor functions, functions with other special properties
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
autor
- 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
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