Ways of checking pointwise convergence
up vote
0
down vote
favorite
According to the definition of pointwise convergence:
A sequence $f_m(x)$ of real valued functions defined on D a subset of real numbers
is said to be pointwise convergent to$f(d)$ at a point $depsilon D$ if for all $epsilon$>0 there exists a $m_0$ such that $|f_m(d)-f(d)|$<$epsilon$ for all $m>m_0$
to check pointwise convergence a given interval for a given function , do we need to do all this work above? or we can simply find the $lim mto$infinity for the function $f_m(x)$ and if it exists then say that the function is pointwise convergent?
real-analysis pointwise-convergence sequence-of-function
asked Nov 23 at 23:15
Cosmic
569
add a comment |
up vote
0
down vote
favorite
According to the definition of pointwise convergence:
A sequence $f_m(x)$ of real valued functions defined on D a subset of real numbers
is said to be pointwise convergent to$f(d)$ at a point $depsilon D$ if for all $epsilon$>0 there exists a $m_0$ such that $|f_m(d)-f(d)|$<$epsilon$ for all $m>m_0$
to check pointwise convergence a given interval for a given function , do we need to do all this work above? or we can simply find the $lim mto$infinity for the function $f_m(x)$ and if it exists then say that the function is pointwise convergent?
real-analysis pointwise-convergence sequence-of-function
asked Nov 23 at 23:15
Cosmic
569
1
It's the same thing. If you find $lim_{m to infty} f_m(d) = f(d)$ for all $d$ and write down the formal definition of limit, you'll just get what's in your first paragraph.
– angryavian
Nov 24 at 0:21
Thanks a lot for the help:)
– Cosmic
Nov 24 at 0:22
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
According to the definition of pointwise convergence:
A sequence $f_m(x)$ of real valued functions defined on D a subset of real numbers
is said to be pointwise convergent to$f(d)$ at a point $depsilon D$ if for all $epsilon$>0 there exists a $m_0$ such that $|f_m(d)-f(d)|$<$epsilon$ for all $m>m_0$
to check pointwise convergence a given interval for a given function , do we need to do all this work above? or we can simply find the $lim mto$infinity for the function $f_m(x)$ and if it exists then say that the function is pointwise convergent?
real-analysis pointwise-convergence sequence-of-function
asked Nov 23 at 23:15
Cosmic
569
According to the definition of pointwise convergence:
A sequence $f_m(x)$ of real valued functions defined on D a subset of real numbers
is said to be pointwise convergent to$f(d)$ at a point $depsilon D$ if for all $epsilon$>0 there exists a $m_0$ such that $|f_m(d)-f(d)|$<$epsilon$ for all $m>m_0$
to check pointwise convergence a given interval for a given function , do we need to do all this work above? or we can simply find the $lim mto$infinity for the function $f_m(x)$ and if it exists then say that the function is pointwise convergent?
real-analysis pointwise-convergence sequence-of-function
real-analysis pointwise-convergence sequence-of-function
asked Nov 23 at 23:15
Cosmic
569
asked Nov 23 at 23:15
Cosmic
569
asked Nov 23 at 23:15
Cosmic
569
asked Nov 23 at 23:15
Cosmic
569
asked Nov 23 at 23:15
Cosmic
569
569
1
It's the same thing. If you find $lim_{m to infty} f_m(d) = f(d)$ for all $d$ and write down the formal definition of limit, you'll just get what's in your first paragraph.
– angryavian
Nov 24 at 0:21
Thanks a lot for the help:)
– Cosmic
Nov 24 at 0:22
add a comment |
1
It's the same thing. If you find $lim_{m to infty} f_m(d) = f(d)$ for all $d$ and write down the formal definition of limit, you'll just get what's in your first paragraph.
– angryavian
Nov 24 at 0:21
Thanks a lot for the help:)
– Cosmic
Nov 24 at 0:22
1
1
It's the same thing. If you find $lim_{m to infty} f_m(d) = f(d)$ for all $d$ and write down the formal definition of limit, you'll just get what's in your first paragraph.
– angryavian
Nov 24 at 0:21
It's the same thing. If you find $lim_{m to infty} f_m(d) = f(d)$ for all $d$ and write down the formal definition of limit, you'll just get what's in your first paragraph.
– angryavian
Nov 24 at 0:21
Thanks a lot for the help:)
– Cosmic
Nov 24 at 0:22
Thanks a lot for the help:)
– Cosmic
Nov 24 at 0:22
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3010958%2fways-of-checking-pointwise-convergence%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
It's the same thing. If you find $lim_{m to infty} f_m(d) = f(d)$ for all $d$ and write down the formal definition of limit, you'll just get what's in your first paragraph.
– angryavian
Nov 24 at 0:21
Thanks a lot for the help:)
– Cosmic
Nov 24 at 0:22