Bibliography for Riemann Sums

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  1. Construction of concentration measures for general Lorenz curves using Riemann-Stieltjes integrals.  
    Egghe, L.
    Math. Comput. Modelling  35  (2002),  no. 9-10, 1149--1163, MathSciNet.  
  2. Partitions of the interval in the definition of Riemann's integral  
    Tong, J.
    International Journal of Mathematical Education in Science and Technology, 2001, vol. 32, no. 5, pp. 788-792, Ingenta.   
  3. A Convergence Theorem for the Riemann Integral  
    Gordon, Russell A.
    Mathematics Magazine, 2000, vol. 73, no. 2, pp. 141, Ingenta.   
  4. Approximating a Riemann integral using the central limit theorem.
    Tunaru, R.
    Mathematica japonicae [sic], 1999, vol. 49, no. 2, pp. 191, Ingenta.   
  5. The improper fuzzy Riemann integral and its numerical integration.
    Wu, Hsien-Chung
    Information sciences, 1998, vol. 111, no. 1/4, pp. 109-13, Ingenta.   
  6. A Riemann-type integral based on the second symmetric derivative.
    Freiling, C.; Rinne, D.; Thomson, B.S.
    Journal of the London Mathematical Society, 1997, vol. 56p3, pp. 539, Ingenta.   
  7. Return to the Riemann Integral  
    Robert G. Bartle
    The American Mathematical Monthly, Vol. 103, No. 8. (Oct., 1996), pp. 625-632, Jstor.  
  8. Randomly Sampled Riemann Sums and Complete Convergence in the Law of Large Numbers for a Case without Identical Distribution  
    Alexander R. Pruss
    Proceedings of the American Mathematical Society, Vol. 124, No. 3. (Mar., 1996), pp. 919-929, Jstor.  
  9. A constructive definition of the n-dimensional-integral in terms of Riemann sums.
    Nonnenmacher, Dirk Jens F.
    Real Anal. Exchange 21 (1995/96), no. 1, 216--235, MathSciNet.  
  10. Riemann Sums and the Exponential Function (in Classroom Capsules)  
    Sheldon P. Gordon
    The College Mathematics Journal, Vol. 25, No. 1. (Jan., 1994), pp. 39-40, Jstor.  
  11. Evaluating Lebesgue integrals as limits of Riemann sums.
    Kahane, Charles S.
    Math. Japon. 38 (1993), no. 6, 1073--1076, MathSciNet.  
  12. A concept of absolute continuity and a Riemann type integral.
    Bongiorno, B.; Pfeffer, W.F.
    Commentationes mathematicae Universitatis Carolinae, 1992, vol. 33, no. 2, pp. 189, Ingenta.   
  13. On approximating Lebesgue integrals by Riemann sums.
    Révész, Szilárd Gy.; Ruzsa, Imre Z.
    Glasgow Math. J. 33 (1991), no. 2, 129--134, MathSciNet.  
  14. Hake's property of a multidimensional generalized Riemann integral.
    Mawhin, Jean
    Czechoslovak mathematical journal, 1990, vol. 40, no. 4, pp. 690, Ingenta.   
  15. Taylor's Theorem Using the Generalized Riemann Integral (in The Teaching of Mathematics)  
    H. B. Thompson  
    The American Mathematical Monthly, Vol. 96, No. 4. (Apr., 1989), pp. 346-350, Jstor.  
  16. Riemann Integral of cos x (in Classroom Capsules)  
    John H. Mathews; Harris S. Shultz
    The College Mathematics Journal, Vol. 20, No. 3. (May, 1989), p. 237, Jstor.  
  17. A Note on the Generalized Riemann Integral  
    Washek F. Pfeffer  
    Proceedings of the American Mathematical Society, Vol. 103, No. 4. (Aug., 1988), pp. 1161-1166, Jstor.  
  18. A Geometric Interpretation of the Riemann-Stieltjes Integral (in The Teaching of Mathematics)  
    Gregory L. Bullock  
    The American Mathematical Monthly, Vol. 95, No. 5. (May, 1988), pp. 448-455, Jstor.  
  19. A comparison of two generalizations of the Riemann integral.
    Rutledge, D. S.; Worth, R. E.
    Real Anal. Exchange 13 (1987/88), no. 2, 432--435, MathSciNet.  
  20. A Note on Evaluating Limits Using Riemann Sums (in Notes)  
    Sudhir K. Goel; Dennis M. Rodriguez
    Mathematics Magazine, Vol. 60, No. 4. (Oct., 1987), pp. 225-228, Jstor.  
  21. An Easy Generalization of the Riemann Integral (in The Teaching of Mathematics)  
    Michael W. Botsko  
    The American Mathematical Monthly, Vol. 93, No. 9. (Nov., 1986), pp. 728-732, Jstor.  
  22. Using Riemann Sums in Evaluating a Familiar Limit (in Classroom Capsules)  
    Frank Burk; Sudhir K. Goel; Dennis M. Rodriguez
    The College Mathematics Journal, Vol. 17, No. 2. (Mar., 1986), pp. 170-171, Jstor.  
  23. What is a Differential? A New Answer from the Generalized Riemann Integral  
    Solomon Leader  
    The American Mathematical Monthly, Vol. 93, No. 5. (May, 1986), pp. 348-356, Jstor.  
  24. Riemann sums and improper integrals of step functions related to the prime number theorem.
    Byrnes, J. S.; Giroux, A.; Shisha, O.
    J. Approx. Theory 40 (1984), no. 2, 180--192, MathSciNet.  
  25. Nonstandard Construction of the Stochastic Integral and Applications to Stochastic Differential Equations. I  
    Douglas N. Hoover; Edwin Perkins
    Transactions of the American Mathematical Society, Vol. 275, No. 1. (Jan., 1983), pp. 1-36, Jstor.  
  26. The Lebesgue Integral as the Almost Sure Limit of Random Riemann Sums  
    John C. Kieffer; Caslav V. Stanojevic
    Proceedings of the American Mathematical Society, Vol. 85, No. 3. (Jul., 1982), pp. 389-392, Jstor.  
  27. Riemann sums for stochastic integrals and Lp moduli of continuity.
    Sjögren, Peter
    Z. Wahrsch. Verw. Gebiete 59 (1982), no. 3, 411--424, MathSciNet.  
  28. Shorter Notes: The Riemann Integral in Constructive Mathematics  
    David Spring
    Proceedings of the American Mathematical Society, Vol. 83, No. 4. (Dec., 1981), pp. 839-840, Jstor.  
  29. How Close Are the Riemann Sums to the Integral They Approximate? (in Classroom Capsules)  
    V. N. Murty
    The Two-Year College Mathematics Journal, Vol. 11, No. 4. (Sep., 1980), pp. 268-270, Jstor.  
  30. Regulated Functions: Bourbaki's Alternative to the Riemann Integral (in Classroom Notes)  
    S. K. Berberian
    The American Mathematical Monthly, Vol. 86, No. 3. (Mar., 1979), pp. 208-211, Jstor.  
  31. Infinite Riemann sums, the simple integral, and the dominated integral.
    Lewis, James T.; Osgood, Charles F.; Shisha, Oved
    General inequalities (Proc. First Internat. Conf., Math. Res. Inst., Oberwolfach, 1976), I, pp. 233--242. Birkhäuser, Basel, 1978, MathSciNet.  
  32. Arzela's Dominated Convergence Theorem for the Riemann Integral  
    W. A. J. Luxemburg
    The American Mathematical Monthly, Vol. 78, No. 9. (Nov., 1971), pp. 970-979, Jstor.  
  33. An Inequality for the Riemann-Stieltjes Integral  
    Richard Darst; Harry Pollard
    Proceedings of the American Mathematical Society, Vol. 25, No. 4. (Aug., 1970), pp. 912-913, Jstor.  
  34. On a Riemann Sum Construction of Rudin  
    C. J. Mozzochi
    Proceedings of the American Mathematical Society, Vol. 22, No. 3. (Sep., 1969), p. 718, Jstor.  
  35. On the Nature of Certain Quadrature Formulas and Their Errors  
    Christopher T. H. Baker  
    SIAM Journal on Numerical Analysis, Vol. 5, No. 4. (Dec., 1968), pp. 783-804, Jstor.  
  36. Numerical Integration and Riemann-Stieltjes Sums  
    Henry P. Decell, Jr.; Robert N. Lea
    SIAM Review, Vol. 8, No. 2. (Apr., 1966), pp. 196-200, Jstor.  
  37. Numerical Integration and the Solution of Integral Equations by the Use of Riemann Sums  
    L. B. Rall
    SIAM Review, Vol. 7, No. 1. (Jan., 1965), pp. 55-64, Jstor.  
  38. On the Riemann Integral in Two Dimensions (in Classroom Notes)  
    Solomon Marcus
    The American Mathematical Monthly, Vol. 71, No. 5. (May, 1964), pp. 544-545, Jstor.  
  39. An Arithmetic Property of Riemann Sums  
    Walter Rudin
    Proceedings of the American Mathematical Society, Vol. 15, No. 2. (Apr., 1964), pp. 321-324, Jstor.  
  40. On the Definition of the Riemann Integral (in Classroom Notes)  
    Abe Sklar
    The American Mathematical Monthly, Vol. 67, No. 9. (Nov., 1960), pp. 897-900, Jstor.  
  41. On a new definition of stochastic integral by random Riemann sum.
    Nisio, Makiko
    Mem. Coll. Sci. Univ. Kyoto. Ser. A. Math. 31 1958 25--31, MathSciNet.  
  42. A Generalization of the Riemann Integral  
    Casper Goffman  
    Proceedings of the American Mathematical Society, Vol. 3, No. 4. (Aug., 1952), pp. 543-547, Jstor.  
  43. Convergence of Cauchy-Riemann sums to Cauchy-Riemann integrals.
    0a Szász, Otto; Todd, John
    J. Research Nat. Bur. Standards 47, (1951). 191--196, MathSciNet.  
  44. A Note on the Riemann Integral (in Discussions and Notes)  
    H. E. Robbins
    The American Mathematical Monthly, Vol. 50, No. 10. (Dec., 1943), pp. 617-618, Jstor.  
  45. Approximative Riemann-sums for improper integrals.
    Dickinson, D. R.
    Quart. J. Math., Oxford Ser. 12, (1941). 176--183, MathSciNet.  
  46. Definite Integrals and Riemann Sums  
    J. A. Shohat
    The American Mathematical Monthly, Vol. 46, No. 9. (Nov., 1939), pp. 538-545, Jstor.  
  47. Note on Degree of Approximation to an Integral by Riemann Sums  
    J. L. Wals; W. E. Sewell
    The American Mathematical Monthly, Vol. 44, No. 3. (Mar., 1937), pp. 155-160, Jstor.  
  48. On the Approximation of Lebesgue Integrals by Riemann Sums  
    B. Jessen
    The Annals of Mathematics, 2nd Ser., Vol. 35, No. 2. (Apr., 1934), pp. 248-251, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004