International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B, ch. 1.3, p. 35   | 1 | 2 |

## Section 1.3.2.4.2.7. Riemann–Lebesgue lemma

G. Bricognea

aMRC Laboratory of Molecular Biology, Hills Road, Cambridge CB2 2QH, England, and LURE, Bâtiment 209D, Université Paris-Sud, 91405 Orsay, France

#### 1.3.2.4.2.7. Riemann–Lebesgue lemma

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If , i.e. is summable, then and exist and are continuous and essentially bounded: In fact one has the much stronger property, whose statement constitutes the Riemann–Lebesgue lemma, that and both tend to zero as .