## Real Analysis Exchange

### On Henstockʼs Inner Variation and Strong Derivatives

Chew Tuan Seng

#### Abstract

The Lebesgue and Bochner integrals are characterized by strong derivatives, inner variation and Lusin condition in this note.

#### Article information

Source
Real Anal. Exchange, Volume 27, Number 2 (2001), 725-734.

Dates
First available in Project Euclid: 2 June 2008

https://projecteuclid.org/euclid.rae/1212412868

Mathematical Reviews number (MathSciNet)
MR1923161

Zentralblatt MATH identifier
1069.26008

#### Citation

Seng, Chew Tuan. On Henstockʼs Inner Variation and Strong Derivatives. Real Anal. Exchange 27 (2001), no. 2, 725--734. https://projecteuclid.org/euclid.rae/1212412868

#### References

• C. L. Belna, M. J. Evans and P. D. Humke, Symmetric and Strong Differentiation, Amer. Math. Monthly, 86 (1979), 121–123.
• E. Cabral and Lee Peng Yee, A Fundamental Theorem of Calculus for the Kurzweil-Henstock Integrals in $\mathbb R^m$, Real Anal. Exchange, 26(2) (2000–2001), 867–876.
• J. Diestel and J. J. Uhl Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., 1977.
• M. Esser and O. Shisha, A Modified Differentiation, Amer. Math. Monthly, 71 (1964), 904–906.
• Jean-Christophe Feauveau, A Generalized Riemann Integral for Banach-Valued Functions, Real Anal. Exchange, 25(2) (1999–2000), 919–930.
• R. Henstock, The General Theory of Integration, Oxford University Press, Oxford, 1991.
• Lu Jitan and Lee Peng Yee, The Primitive of Henstock Integrals Functions in Euclidean Space, Bull. London Math. Society, 31 (1999), 173–180.
• Ma Zhengmin, Lee Peng Yee and Chew Tuan Seng, Absolute Integration Using Vitali Covers, Real Anal. Exchange, 18(2) (1992–93), 405–419.
• J. Mikusinski, The Bockner Integral, Birkhauser, 1978.
• Nakanishi Shizu, {The Henstock Integral for Functions with Values in Nuclear Spaces and the Henstock
• A. P. Solodov, On Conditions of Differentiability Almost Everywhere for Absolutely Continuous Banach-Valued Function, Moscow Univ. Math. Bull., 54 (1999), 29–32.
• B. S. Thomson, {Derivation Bases and the Real
• Toh T. L. and Chew T. S., A Variational Approach to It's Integral, Proceedings of Symposium on Analysis and Probability 1998, Taiwan, 291–299, World Scientific Press, Singapore, 1999.
• Wu Congxin and Yao Xiaobo, A Riemann-Type Definition of the Bochner Integral, J. Math. Study, 27 (1994), 32–36.
• Xu J. G. and Lee P. Y., Stochastic Integrals of It$\bar o$ and Henstock, Real Anal. Exchange, 18(2) (1992–93), 352–366.
• Yang Keren and Lu Shipan, Strong Derivative and its Consequences, J. Math. Study, 27 (1994), 191–193.