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For such a characteristic function xa we define the integral J\a dx to be m(A).
Since we want our integral to be linear we define to the function /(necessarily
measurable) and if for some infinite subsequence we have J <t> dx = 2 afn(At)
integral to functions not necessarily nonnega- tive. If a function /is nonnegative on
the set A and negative on the complementary set B =<€A we want / / dx to be JA f
dx - fB (-/) dx. Equivalently, write f+(x) = max(f(x), 0),f'(x) = max(-/W, 0). Then/+ ...
sidered on (0, 1), as one point does not affect the integral, and there it equals So*
"*1 log x. Since 2oJc"+l log 1/x is a series of nonnegative functions we may
integrate it term by term to get 2f l/(« + l)2 as required. EXAMPLE 2. Show that lim
T Jo ...
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Liquid Alkali Metals 1 John F Schenck
Liquid Chromatography 13 Russell L Rasmussen Joseph
Liquid Crystal Devices 41 Manifold Geometry
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