Book Review
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MathSciNet review:
1567219
Full text of review:
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Book Information:
Author:
Andrew M. Bruckner
Title:
Differentiation of real functions
Additional book information:
Lecture Notes in Math., vol. 659, Springer-Verlag, Berlin and New York, 1978, x + 246 pp., $12.00.
A. M. Bruckner and K. M. Garg, The level structure of a residual set of continuous functions, Trans. Amer. Math. Soc. 232 (1977), 307–321. MR 476939, DOI 10.1090/S0002-9947-1977-0476939-X
A. M. Bruckner and C. Goffman, Differentiability through change of variables, Proc. Amer. Math. Soc. 61 (1976), no. 2, 235–241 (1977). MR 432831, DOI 10.1090/S0002-9939-1976-0432831-2
Richard J. Fleissner and James Foran, Transformations of differentiable functions, Colloq. Math. 39 (1978), no. 2, 277–284. MR 522368, DOI 10.4064/cm-39-2-277-284
4. V. Jarnik, Sur les nombres dérivés approximatifs, Fund. Math. 22 (1934), 4-16.
M. Laczkovich and G. Petruska, On the transformers of derivatives, Fund. Math. 100 (1978), no. 3, 179–199. MR 509545, DOI 10.4064/fm-100-3-179-199
J. S. Lipiński, Une propriété des ensembles $\{f’(x)>a\}$, Fund. Math. 42 (1955), 339–342 (French). MR 76842, DOI 10.4064/fm-42-2-339-342
7. J. Marcinkiewicz, Sur les nombres dérivés, Fund. Math. 24 (1935), 305-308.
I. P. Natanson, Theory of functions of a real variable. Vol. II, Frederick Ungar Publishing Co., New York, 1961. Translated from the Russian by Leo F. Boron. MR 0148805
C. J. Neugebauer, Darboux functions of Baire class one and derivatives, Proc. Amer. Math. Soc. 13 (1962), 838–843. MR 143850, DOI 10.1090/S0002-9939-1962-0143850-8
Richard J. O’Malley, The set where an approximate derivative is a derivative, Proc. Amer. Math. Soc. 54 (1976), 122–124. MR 390143, DOI 10.1090/S0002-9939-1976-0390143-X
Richard J. O’Malley and Clifford E. Weil, The oscillatory behavior of certain derivatives, Trans. Amer. Math. Soc. 234 (1977), no. 2, 467–481. MR 453940, DOI 10.1090/S0002-9947-1977-0453940-3
D. Preiss, On the first derivative of real functions, Comment. Math. Univ. Carolinae 11 (1970), 817–822. MR 274669
13. S. Saks, Theory of the integral, Mongrafie Mat., vol. 7, Warszawa, 1937.
14. W. Sierpiński, Sur une propriété de fonctions quelconques d'une variable réelle, Fund. Math. 25 (1935), 1-14.
Clifford E. Weil, On properties of derivatives, Trans. Amer. Math. Soc. 114 (1965), 363–376. MR 176007, DOI 10.1090/S0002-9947-1965-0176007-2
Clifford E. Weil, On approximate and Peano derivatives, Proc. Amer. Math. Soc. 20 (1969), 487–490. MR 233944, DOI 10.1090/S0002-9939-1969-0233944-7
Hassler Whitney, On totally differentiable and smooth functions, Pacific J. Math. 1 (1951), 143–159. MR 43878
Z. Zahorski, Sur la première dérivée, Trans. Amer. Math. Soc. 69 (1950), 1–54 (French). MR 37338, DOI 10.1090/S0002-9947-1950-0037338-9
- 1.
- A. Bruckner and K. Garg, The level structure of a residual set of continuous functions, Trans. Amer. Math. Soc. 232 (1977), 307-321. MR 0476939
- 2.
- A. Bruckner and C. Goffman, Differentiability through change of variables, Proc. Amer. Math. Soc. 61 (1976), 235-241. MR 432831
- 3.
- R. Fleissner and J. Foran, Transformations of differentiable functions, Colloq. Math. 39 (1978), 277-284. MR 522368
- 4.
- V. Jarnik, Sur les nombres dérivés approximatifs, Fund. Math. 22 (1934), 4-16.
- 5.
- M. Laczkovich and G. Petruska, On the transformers of derivatives, Fund. Math. 100 (1978), 179-199. MR 509545
- 6.
- J. Lipiński, Une propriété des ensembles {ƒ'(x)>a}, Fund. Math. 42 (1955), 339-342. MR 76842
- 7.
- J. Marcinkiewicz, Sur les nombres dérivés, Fund. Math. 24 (1935), 305-308.
- 8.
- I. Natanson, Theory of functions of a real variable, Vol. I, Ungar, New York, 1961. MR 148805
- 9.
- C. Neugebauer, Darboux functions of Baire class 1 and derivatives, Proc. Amer. Math. Soc. 13 (1962), 838-843. MR 143850
- 10.
- R. O'Malley, The set where the approximate derivative is a derivative, Proc. Amer. Math. Soc. 54 (1976), 122-124. MR 390143
- 11.
- R. O'Malley and C. Weil, The oscillatory behavior of certain derivatives, Trans. Amer. Math. Soc. 234 (1977), 467-481. MR 453940
- 12.
- D. Preiss, On the first derivative of real functions, Comm. Math. Univ. Carolinae 11 (1974), 817-822. MR 274669
- 13.
- S. Saks, Theory of the integral, Mongrafie Mat., vol. 7, Warszawa, 1937.
- 14.
- W. Sierpiński, Sur une propriété de fonctions quelconques d'une variable réelle, Fund. Math. 25 (1935), 1-14.
- 15.
- C. Weil, On properties of derivatives, Trans. Amer. Math. Soc. 114 (1965), 363-376. MR 176007
- 16.
- C. Weil, On approximate and Peano derivatives, Proc. Amer. Math. Soc. 20 (1969), 487-490. MR 233944
- 17.
- H. Whitney, On totally differentiate and smooth functions, Pacific J. Math. 1 (1951), 143-159. MR 43878
- 18.
- Z. Zahorski, Sur la première dérivée, Trans. Amer. Math. Soc. 69 (1950), 1-54. MR 37338
Review Information:
Reviewer:
Daniel Waterman
Journal:
Bull. Amer. Math. Soc.
2 (1980), 232-237
DOI:
https://doi.org/10.1090/S0273-0979-1980-14733-3