Even more on the fundamental theorem of calculus


  • Charles Swartz New Mexico State University, New Mexico.




Lipschitz, Botsko, Integrales


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.


Author Biography

Charles Swartz, New Mexico State University, New Mexico.

Department of Mathemical Sciences.


[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.



How to Cite

C. Swartz, “Even more on the fundamental theorem of calculus”, Proyecciones (Antofagasta, On line), vol. 12, no. 2, pp. 129-135, Apr. 2018.