Abstract
Let f(x) be a bounded function on the finite interval [a, b]. The points with abscissae x0, x1, x2,…,xn−1, xn where
constitute a subdivision of this interval. Denote by m v and M v the greatest lower and the least upper bound, respectively, of f(x) on the v-th subinterval [x v −1, x v ], v= 1,2,…, n. We call
belonging to the subdivision x0, x1, x2,…, xn−1, x n . Any upper sum is always larger (not smaller) than any lower sum, regardless of the subdivision considered.
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© 1998 Springer-Verlag Berlin Heidelberg
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Pólya, G., Szegö, G. (1998). The Integral as the Limit of a Sum of Rectangles. In: Problems and Theorems in Analysis I. Classics in Mathematics, vol 193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61983-0_5
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DOI: https://doi.org/10.1007/978-3-642-61983-0_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63640-3
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