Establish uniform convergence
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Let ${f_n}$ be a decreasing sequence of continuous functions, which converges to a continuous function $f$ on a compact set $E$. Prove that $f_n to f$ uniformly on $E$.
real-analysis compactness uniform-convergence
edited Nov 16 at 2:10
gt6989b
32.1k22351
asked Nov 16 at 2:01
Swadiq KLG
6
add a comment |
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Let ${f_n}$ be a decreasing sequence of continuous functions, which converges to a continuous function $f$ on a compact set $E$. Prove that $f_n to f$ uniformly on $E$.
real-analysis compactness uniform-convergence
edited Nov 16 at 2:10
gt6989b
32.1k22351
asked Nov 16 at 2:01
Swadiq KLG
6
3
What have you tried? Where did you get stuck?
– rldias
Nov 16 at 2:03
1
This is Dini theorem
– Shubham
Nov 16 at 4:35
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let ${f_n}$ be a decreasing sequence of continuous functions, which converges to a continuous function $f$ on a compact set $E$. Prove that $f_n to f$ uniformly on $E$.
real-analysis compactness uniform-convergence
edited Nov 16 at 2:10
gt6989b
32.1k22351
asked Nov 16 at 2:01
Swadiq KLG
6
Let ${f_n}$ be a decreasing sequence of continuous functions, which converges to a continuous function $f$ on a compact set $E$. Prove that $f_n to f$ uniformly on $E$.
real-analysis compactness uniform-convergence
real-analysis compactness uniform-convergence
edited Nov 16 at 2:10
gt6989b
32.1k22351
asked Nov 16 at 2:01
Swadiq KLG
6
edited Nov 16 at 2:10
gt6989b
32.1k22351
asked Nov 16 at 2:01
Swadiq KLG
6
edited Nov 16 at 2:10
gt6989b
32.1k22351
edited Nov 16 at 2:10
gt6989b
32.1k22351
edited Nov 16 at 2:10
gt6989b
32.1k22351
32.1k22351
asked Nov 16 at 2:01
Swadiq KLG
6
asked Nov 16 at 2:01
Swadiq KLG
6
asked Nov 16 at 2:01
Swadiq KLG
6
6
3
What have you tried? Where did you get stuck?
– rldias
Nov 16 at 2:03
1
This is Dini theorem
– Shubham
Nov 16 at 4:35
add a comment |
3
What have you tried? Where did you get stuck?
– rldias
Nov 16 at 2:03
1
This is Dini theorem
– Shubham
Nov 16 at 4:35
3
3
What have you tried? Where did you get stuck?
– rldias
Nov 16 at 2:03
What have you tried? Where did you get stuck?
– rldias
Nov 16 at 2:03
1
1
This is Dini theorem
– Shubham
Nov 16 at 4:35
This is Dini theorem
– Shubham
Nov 16 at 4:35
add a comment |
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3
What have you tried? Where did you get stuck?
– rldias
Nov 16 at 2:03
1
This is Dini theorem
– Shubham
Nov 16 at 4:35