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Therefore M is summable.
A module M is summable and a strong ω-elongation of a totally projective module by a (ω+1 -projective module if and only if M is a totally projective module of length ≤ω+1 -projective
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Since, the sequence is summable.
which is summable over n.
Since is summable, so is, and hence.
In particular, ( ( S z α ) α ∈ Λ < b is summable.
Consequently, lim β → γ − σ exists, so that ( ( S z α ) α ∈ Λ < γ is summable.
Thus, if ( z α ( n 0, …, n m ) ) α ( n 0, …, n m ) ∈ Λ m is such a family of real numbers that the family ( 2 − ∑ k = 0 m n k − m − 1 z α ( n 0, …, n m ) ) α ( n 0, …, n m ) ∈ Λ m. is summable, then the mapping g : [ 0, 1 ] → E, defined by. is HL integrable by Proposition 3.1.
Then ∑ a n λ n is summable | R, q n | k, k ≥ 1 whenever ∑ a n is summable | R, p n |, if and only if (10) (11).
Then, in order that ∑ a n λ n is summable | B | k whenever ∑ a n is summable | A |, it is necessary that (19).
then ∑ a n λ n is summable | N ¯, p n | k, k ≥ 1.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com