Ciro Santilli
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L
p
norm sequence convergence does not imply pointwise convergence
Fourier basis is complete for
L
2
nosplit
words:
40
math.stackexchange.com/questions/138043/does-convergence-in-lp-imply-convergence-almost-everywhere
There are explicit examples of this. We can have ever thinner disturbances to convergence that keep getting less and less area, but never cease to move around.
If it does converge pointwise to something, then it must match of course.
Ancestors
Fourier basis is complete for
L
2
Riesz-Fischer theorem
Lebesgue integral of
L
p
is complete but Riemann isn't
Lebesgue integral
Integral
Calculus
Mathematics
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Fourier basis is complete for
L
2