Timeline for For every monotonically-decreasing non-negative function $ f $, does there exist a function $ g $ so that $ f g $ is integrable?
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| Apr 19, 2017 at 18:04 | comment | added | Willie Wong | One can also remark that by the "integral test" for series convergence, the original question posed is equivalent to asking whether for every monotonically decreasing-to-zero sequence $(f_n)$ there exists a sequence $(g_n)$ such that $\sum g_n$ diverges but $\sum f_n g_n$ converges. And the final construction can then be regarded as the finite difference version of the "derivative method" mentioned in the first paragraph. | |
| Apr 19, 2017 at 17:59 | history | answered | Will Sawin | CC BY-SA 3.0 |