Even more on the fundamental theorem of calculus
DOI:
https://doi.org/10.22199/S07160917.1993.0002.00003Keywords:
Lipschitz, Botsko, IntegralesAbstract
We show that the general form of the Fundamental Theorem of Calculus for Lipschitz functions derived by Botsko [B2] is valid for the gauge integral and
can be obtained by very elementary means.
References
[B1] Botsko, M.: An elementary proof that a bounded a.e. continuous function is Riemann integrable. Amer. Math. Monthly, 95 (1988), 249-252.
[B2] Botsko, M.: A Fundamental Theorem of Calculus that applies to all Riemann integrable functions. Math. Mag., 64 (1991), 347-348.
[DS] DePree, J.; Swartz, C.: Introduction to Real Analysis. Wiley, N. Y., 1987.
[H] Henstock, R.: Definitions of Riemann type of the variational integrals. Proc. London Math. Soc., 11(1961), 402-418.
[HS] Hewitt, E.; Stromberg, K.: Real and Abstract Analysis. Springer- Verlag, Heidelberg, 1965.
[K] Kurzweil, J.: Generalized ordinary differential equations and continuous dependence on a parameter. Czech. Math. J., 82 (1957), 418-449.
[L] Lee Peng Yee: Lanzhou Lectures on Henstock Integration. World Scientific Publs., Singapore, 1989.
[Mc] McLeod, R.: The Generalized Riemann Integral. Carus Math. Monograph 20, MAA, 1980.
[ST] Swartz, C.; Thomson, B.: More on the Fundamental Theorem of Calculus. Amer. Math. Monthly, 95 (1988), 644-648.
[B2] Botsko, M.: A Fundamental Theorem of Calculus that applies to all Riemann integrable functions. Math. Mag., 64 (1991), 347-348.
[DS] DePree, J.; Swartz, C.: Introduction to Real Analysis. Wiley, N. Y., 1987.
[H] Henstock, R.: Definitions of Riemann type of the variational integrals. Proc. London Math. Soc., 11(1961), 402-418.
[HS] Hewitt, E.; Stromberg, K.: Real and Abstract Analysis. Springer- Verlag, Heidelberg, 1965.
[K] Kurzweil, J.: Generalized ordinary differential equations and continuous dependence on a parameter. Czech. Math. J., 82 (1957), 418-449.
[L] Lee Peng Yee: Lanzhou Lectures on Henstock Integration. World Scientific Publs., Singapore, 1989.
[Mc] McLeod, R.: The Generalized Riemann Integral. Carus Math. Monograph 20, MAA, 1980.
[ST] Swartz, C.; Thomson, B.: More on the Fundamental Theorem of Calculus. Amer. Math. Monthly, 95 (1988), 644-648.
Published
2018-04-03
How to Cite
[1]
C. Swartz, “Even more on the fundamental theorem of calculus”, Proyecciones (Antofagasta, On line), vol. 12, no. 2, pp. 129-135, Apr. 2018.
Issue
Section
Artículos
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.