Everything about Absolute Convergence totally explained
In
mathematics, a
series (or sometimes also an
integral) is said to
converge absolutely if the sum (or integral) of the
absolute value of the summand or integrand is
finite.
More precisely, a real or complex-valued series
is the set of natural numbers,
Lebesgue integrability, unordered summability and absolute convergence all coincide.
Finally, all of the above holds for integrals with values in a Banach space. The definition
of a Banach-valued Riemann integral is an evident modification of the usual one. For the
Lebesgue integral one needs to circumvent the decomposition into positive and negative parts
with Daniell's more functional analytic approach, obtaining the
Bochner integral.
Further Information
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