convergence of the limit of $int f_n(x) dx$ on $(0,infty)$ [on hold]
Suppose $f_n$ integrable on $(0,infty)$ for all n, and $f_n to f$ uniformly. Then is f integrable on $(0,infty)$? Does $int f_n(x) dx$ exist on $(0,infty)$?
Rudin proved the case on $[a,b]$ (theorem 7.16). But can we extend it to $(0,infty)$? I couldn't prove it ...
analysis
edited Dec 26 at 15:18
gt6989b
33k22452
asked Dec 26 at 14:49
aud999
853
put on hold as off-topic by mrtaurho, gammatester, José Carlos Santos, Saad, RRL Dec 26 at 15:14
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – mrtaurho, gammatester, José Carlos Santos, Saad, RRL
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
Suppose $f_n$ integrable on $(0,infty)$ for all n, and $f_n to f$ uniformly. Then is f integrable on $(0,infty)$? Does $int f_n(x) dx$ exist on $(0,infty)$?
Rudin proved the case on $[a,b]$ (theorem 7.16). But can we extend it to $(0,infty)$? I couldn't prove it ...
analysis
edited Dec 26 at 15:18
gt6989b
33k22452
asked Dec 26 at 14:49
aud999
853
put on hold as off-topic by mrtaurho, gammatester, José Carlos Santos, Saad, RRL Dec 26 at 15:14
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – mrtaurho, gammatester, José Carlos Santos, Saad, RRL
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
Suppose $f_n$ integrable on $(0,infty)$ for all n, and $f_n to f$ uniformly. Then is f integrable on $(0,infty)$? Does $int f_n(x) dx$ exist on $(0,infty)$?
Rudin proved the case on $[a,b]$ (theorem 7.16). But can we extend it to $(0,infty)$? I couldn't prove it ...
analysis
edited Dec 26 at 15:18
gt6989b
33k22452
asked Dec 26 at 14:49
aud999
853
Suppose $f_n$ integrable on $(0,infty)$ for all n, and $f_n to f$ uniformly. Then is f integrable on $(0,infty)$? Does $int f_n(x) dx$ exist on $(0,infty)$?
Rudin proved the case on $[a,b]$ (theorem 7.16). But can we extend it to $(0,infty)$? I couldn't prove it ...
analysis
analysis
edited Dec 26 at 15:18
gt6989b
33k22452
asked Dec 26 at 14:49
aud999
853
edited Dec 26 at 15:18
gt6989b
33k22452
asked Dec 26 at 14:49
aud999
853
edited Dec 26 at 15:18
gt6989b
33k22452
edited Dec 26 at 15:18
gt6989b
33k22452
edited Dec 26 at 15:18
gt6989b
33k22452
33k22452
asked Dec 26 at 14:49
aud999
853
asked Dec 26 at 14:49
aud999
853
asked Dec 26 at 14:49
aud999
853
853
put on hold as off-topic by mrtaurho, gammatester, José Carlos Santos, Saad, RRL Dec 26 at 15:14
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – mrtaurho, gammatester, José Carlos Santos, Saad, RRL
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by mrtaurho, gammatester, José Carlos Santos, Saad, RRL Dec 26 at 15:14
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – mrtaurho, gammatester, José Carlos Santos, Saad, RRL
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
add a comment |
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