“Famille sommable” in English
In French, given a normed vector space $(E, Vert cdot Vert)$, we say that a set of vectors $mathcal C = {c_i ; i in I}$ is a "famille sommable" when
$$(forall epsilon > 0) , (exists J_0 in mathcal F(I)) , (forall K in mathcal F(I setminus J_0)) , leftVert displaystyle sum_{k in K} c_k rightVert< epsilon$$
where $mathcal F(A)$ is defined as the sets of finite subsets of $A$.
Is there a similar wording in English? At least Wikipedia page I provided above is not refering to a similar an English page.
Note: this question has for root cause Uncountable sum of vectors in a Hilbert Space.
sequences-and-series terminology
asked 14 hours ago
mathcounterexamples.net
24.9k21753
add a comment |
In French, given a normed vector space $(E, Vert cdot Vert)$, we say that a set of vectors $mathcal C = {c_i ; i in I}$ is a "famille sommable" when
$$(forall epsilon > 0) , (exists J_0 in mathcal F(I)) , (forall K in mathcal F(I setminus J_0)) , leftVert displaystyle sum_{k in K} c_k rightVert< epsilon$$
where $mathcal F(A)$ is defined as the sets of finite subsets of $A$.
Is there a similar wording in English? At least Wikipedia page I provided above is not refering to a similar an English page.
Note: this question has for root cause Uncountable sum of vectors in a Hilbert Space.
sequences-and-series terminology
asked 14 hours ago
mathcounterexamples.net
24.9k21753
en.wikipedia.org/wiki/… ?
– Clement C.
14 hours ago
add a comment |
In French, given a normed vector space $(E, Vert cdot Vert)$, we say that a set of vectors $mathcal C = {c_i ; i in I}$ is a "famille sommable" when
$$(forall epsilon > 0) , (exists J_0 in mathcal F(I)) , (forall K in mathcal F(I setminus J_0)) , leftVert displaystyle sum_{k in K} c_k rightVert< epsilon$$
where $mathcal F(A)$ is defined as the sets of finite subsets of $A$.
Is there a similar wording in English? At least Wikipedia page I provided above is not refering to a similar an English page.
Note: this question has for root cause Uncountable sum of vectors in a Hilbert Space.
sequences-and-series terminology
asked 14 hours ago
mathcounterexamples.net
24.9k21753
In French, given a normed vector space $(E, Vert cdot Vert)$, we say that a set of vectors $mathcal C = {c_i ; i in I}$ is a "famille sommable" when
$$(forall epsilon > 0) , (exists J_0 in mathcal F(I)) , (forall K in mathcal F(I setminus J_0)) , leftVert displaystyle sum_{k in K} c_k rightVert< epsilon$$
where $mathcal F(A)$ is defined as the sets of finite subsets of $A$.
Is there a similar wording in English? At least Wikipedia page I provided above is not refering to a similar an English page.
Note: this question has for root cause Uncountable sum of vectors in a Hilbert Space.
sequences-and-series terminology
sequences-and-series terminology
asked 14 hours ago
mathcounterexamples.net
24.9k21753
asked 14 hours ago
mathcounterexamples.net
24.9k21753
asked 14 hours ago
mathcounterexamples.net
24.9k21753
asked 14 hours ago
mathcounterexamples.net
24.9k21753
asked 14 hours ago
mathcounterexamples.net
24.9k21753
24.9k21753
en.wikipedia.org/wiki/… ?
– Clement C.
14 hours ago
add a comment |
en.wikipedia.org/wiki/… ?
– Clement C.
14 hours ago
en.wikipedia.org/wiki/… ?
– Clement C.
14 hours ago
en.wikipedia.org/wiki/… ?
– Clement C.
14 hours ago
add a comment |
1 Answer
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It's a “summable family”. That's the expression that is used in the English version of Bourbaki's General Topology.
answered 14 hours ago
José Carlos Santos
151k22123224
add a comment |
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
It's a “summable family”. That's the expression that is used in the English version of Bourbaki's General Topology.
answered 14 hours ago
José Carlos Santos
151k22123224
add a comment |
It's a “summable family”. That's the expression that is used in the English version of Bourbaki's General Topology.
answered 14 hours ago
José Carlos Santos
151k22123224
add a comment |
It's a “summable family”. That's the expression that is used in the English version of Bourbaki's General Topology.
answered 14 hours ago
José Carlos Santos
151k22123224
It's a “summable family”. That's the expression that is used in the English version of Bourbaki's General Topology.
answered 14 hours ago
José Carlos Santos
151k22123224
answered 14 hours ago
José Carlos Santos
151k22123224
answered 14 hours ago
José Carlos Santos
151k22123224
answered 14 hours ago
José Carlos Santos
151k22123224
151k22123224
add a comment |
add a comment |
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en.wikipedia.org/wiki/… ?
– Clement C.
14 hours ago