In functional analysis, is there a commonly accepted short-hand notation for specific types of convergence?
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In math literature on functional analysis I found various short-hand notations for specific types of convergence, e.g. a single right arrow for pointwise convergence
$$f_n(x) underset{n to infty}{to} f(x)$$
as opposed to paired arrows for uniform convergence
$$f_n(x) underset{n to infty}{⇉} f(x)$$
Are these notations commonly known and accepted? Are there any standard notations to abbreviate clumsy constructs such as
$$ forall varepsilon>0 exists N forall x forall n>N:
|f_n(x)-f(x)|<varepsilon $$
convergence notation uniform-convergence pointwise-convergence
asked Dec 28 '18 at 15:01
user3609959user3609959
212
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add a comment |
$begingroup$
In math literature on functional analysis I found various short-hand notations for specific types of convergence, e.g. a single right arrow for pointwise convergence
$$f_n(x) underset{n to infty}{to} f(x)$$
as opposed to paired arrows for uniform convergence
$$f_n(x) underset{n to infty}{⇉} f(x)$$
Are these notations commonly known and accepted? Are there any standard notations to abbreviate clumsy constructs such as
$$ forall varepsilon>0 exists N forall x forall n>N:
|f_n(x)-f(x)|<varepsilon $$
convergence notation uniform-convergence pointwise-convergence
asked Dec 28 '18 at 15:01
user3609959user3609959
212
$endgroup$
1
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Why not just write it out in text? I feel that writing it out makes it much easier to follow what's going on.
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– MisterRiemann
Dec 28 '18 at 15:03
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Thanks for your comment, MisterRiemann. In my opinion, using expressive symbols and concise formulae in addition to the text may help the reader to grasp and remember the key concepts more easily.
$endgroup$
– user3609959
Dec 28 '18 at 16:00
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Big fan of functional analysis, never seen these notations with those meanings. If you want to use such notation, always explain what you mean. Although I agree with MisterRiemann that you want to avoid defining too many notations. It means the reader has to remember all these notations in order to understand what you're writing about.
$endgroup$
– SmileyCraft
Dec 28 '18 at 19:45
add a comment |
$begingroup$
In math literature on functional analysis I found various short-hand notations for specific types of convergence, e.g. a single right arrow for pointwise convergence
$$f_n(x) underset{n to infty}{to} f(x)$$
as opposed to paired arrows for uniform convergence
$$f_n(x) underset{n to infty}{⇉} f(x)$$
Are these notations commonly known and accepted? Are there any standard notations to abbreviate clumsy constructs such as
$$ forall varepsilon>0 exists N forall x forall n>N:
|f_n(x)-f(x)|<varepsilon $$
convergence notation uniform-convergence pointwise-convergence
asked Dec 28 '18 at 15:01
user3609959user3609959
212
$endgroup$
In math literature on functional analysis I found various short-hand notations for specific types of convergence, e.g. a single right arrow for pointwise convergence
$$f_n(x) underset{n to infty}{to} f(x)$$
as opposed to paired arrows for uniform convergence
$$f_n(x) underset{n to infty}{⇉} f(x)$$
Are these notations commonly known and accepted? Are there any standard notations to abbreviate clumsy constructs such as
$$ forall varepsilon>0 exists N forall x forall n>N:
|f_n(x)-f(x)|<varepsilon $$
convergence notation uniform-convergence pointwise-convergence
convergence notation uniform-convergence pointwise-convergence
asked Dec 28 '18 at 15:01
user3609959user3609959
212
asked Dec 28 '18 at 15:01
user3609959user3609959
212
edited Dec 28 '18 at 15:05
user3609959
asked Dec 28 '18 at 15:01
user3609959user3609959
212
asked Dec 28 '18 at 15:01
user3609959user3609959
212
asked Dec 28 '18 at 15:01
user3609959user3609959
212
212
1
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Why not just write it out in text? I feel that writing it out makes it much easier to follow what's going on.
$endgroup$
– MisterRiemann
Dec 28 '18 at 15:03
$begingroup$
Thanks for your comment, MisterRiemann. In my opinion, using expressive symbols and concise formulae in addition to the text may help the reader to grasp and remember the key concepts more easily.
$endgroup$
– user3609959
Dec 28 '18 at 16:00
$begingroup$
Big fan of functional analysis, never seen these notations with those meanings. If you want to use such notation, always explain what you mean. Although I agree with MisterRiemann that you want to avoid defining too many notations. It means the reader has to remember all these notations in order to understand what you're writing about.
$endgroup$
– SmileyCraft
Dec 28 '18 at 19:45
add a comment |
1
$begingroup$
Why not just write it out in text? I feel that writing it out makes it much easier to follow what's going on.
$endgroup$
– MisterRiemann
Dec 28 '18 at 15:03
$begingroup$
Thanks for your comment, MisterRiemann. In my opinion, using expressive symbols and concise formulae in addition to the text may help the reader to grasp and remember the key concepts more easily.
$endgroup$
– user3609959
Dec 28 '18 at 16:00
$begingroup$
Big fan of functional analysis, never seen these notations with those meanings. If you want to use such notation, always explain what you mean. Although I agree with MisterRiemann that you want to avoid defining too many notations. It means the reader has to remember all these notations in order to understand what you're writing about.
$endgroup$
– SmileyCraft
Dec 28 '18 at 19:45
1
1
$begingroup$
Why not just write it out in text? I feel that writing it out makes it much easier to follow what's going on.
$endgroup$
– MisterRiemann
Dec 28 '18 at 15:03
$begingroup$
Why not just write it out in text? I feel that writing it out makes it much easier to follow what's going on.
$endgroup$
– MisterRiemann
Dec 28 '18 at 15:03
$begingroup$
Thanks for your comment, MisterRiemann. In my opinion, using expressive symbols and concise formulae in addition to the text may help the reader to grasp and remember the key concepts more easily.
$endgroup$
– user3609959
Dec 28 '18 at 16:00
$begingroup$
Thanks for your comment, MisterRiemann. In my opinion, using expressive symbols and concise formulae in addition to the text may help the reader to grasp and remember the key concepts more easily.
$endgroup$
– user3609959
Dec 28 '18 at 16:00
$begingroup$
Big fan of functional analysis, never seen these notations with those meanings. If you want to use such notation, always explain what you mean. Although I agree with MisterRiemann that you want to avoid defining too many notations. It means the reader has to remember all these notations in order to understand what you're writing about.
$endgroup$
– SmileyCraft
Dec 28 '18 at 19:45
$begingroup$
Big fan of functional analysis, never seen these notations with those meanings. If you want to use such notation, always explain what you mean. Although I agree with MisterRiemann that you want to avoid defining too many notations. It means the reader has to remember all these notations in order to understand what you're writing about.
$endgroup$
– SmileyCraft
Dec 28 '18 at 19:45
add a comment |
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$begingroup$
Why not just write it out in text? I feel that writing it out makes it much easier to follow what's going on.
$endgroup$
– MisterRiemann
Dec 28 '18 at 15:03
$begingroup$
Thanks for your comment, MisterRiemann. In my opinion, using expressive symbols and concise formulae in addition to the text may help the reader to grasp and remember the key concepts more easily.
$endgroup$
– user3609959
Dec 28 '18 at 16:00
$begingroup$
Big fan of functional analysis, never seen these notations with those meanings. If you want to use such notation, always explain what you mean. Although I agree with MisterRiemann that you want to avoid defining too many notations. It means the reader has to remember all these notations in order to understand what you're writing about.
$endgroup$
– SmileyCraft
Dec 28 '18 at 19:45