Abstract
If f is a continuous real valued function on [a, b],show that one can approximate f uniformly by step functions whose values are less than or equal to those of f, and also by step functions whose values are greater than or equal to those of f. The integrals of these step functions are then the standard lower and upper Riemann sums.
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© 1998 Springer Science+Business Media New York
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Shakarchi, R. (1998). The Integral in One Variable. In: Problems and Solutions for Undergraduate Analysis. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1738-1_11
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DOI: https://doi.org/10.1007/978-1-4612-1738-1_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98235-9
Online ISBN: 978-1-4612-1738-1
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