Even more on the fundamental theorem of calculus

• Swartz, Charles ^[1]
  1. [1] New Mexico State University

     New Mexico State University

     Estados Unidos

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 12, Nº. 2, 1993, págs. 129-135
• Idioma: inglés
• DOI: 10.22199/S07160917.1993.0002.00003
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• Resumen

  • 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 andcan be obtained by very elementary means. 

• Referencias bibliográficas
  • Citas [B1] Botsko, M.: An elementary proof that a bounded a.e. continuous function is Riemann integrable. Amer. Math. Monthly, 95 (1988),...
  • [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.