there exists a sequence of polynomials which converge uniformly to a continuous f
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If
$lim_{nto {infty}}int_0^1 P_n(x) , dx$ =$int_0^1 f(x) , dx$
(where $P_n(x)$ is a polynomial and f:[0,1]→R)
Can I say directly that
$lim_{nto {infty}}int_0^1 P_n(x)f(x) , dx$ =$int_0^1 f(x)f(x) , dx$
If not, is there a way to prove it?
polynomials definite-integrals
asked Nov 22 at 2:20
kit kat
91
add a comment |
up vote
-1
down vote
favorite
If
$lim_{nto {infty}}int_0^1 P_n(x) , dx$ =$int_0^1 f(x) , dx$
(where $P_n(x)$ is a polynomial and f:[0,1]→R)
Can I say directly that
$lim_{nto {infty}}int_0^1 P_n(x)f(x) , dx$ =$int_0^1 f(x)f(x) , dx$
If not, is there a way to prove it?
polynomials definite-integrals
asked Nov 22 at 2:20
kit kat
91
hint: $f$ is bounded and the convergence is uniform.
– Matematleta
Nov 22 at 2:23
1
Your title and your question are different.
– zhw.
Nov 22 at 3:54
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
If
$lim_{nto {infty}}int_0^1 P_n(x) , dx$ =$int_0^1 f(x) , dx$
(where $P_n(x)$ is a polynomial and f:[0,1]→R)
Can I say directly that
$lim_{nto {infty}}int_0^1 P_n(x)f(x) , dx$ =$int_0^1 f(x)f(x) , dx$
If not, is there a way to prove it?
polynomials definite-integrals
asked Nov 22 at 2:20
kit kat
91
If
$lim_{nto {infty}}int_0^1 P_n(x) , dx$ =$int_0^1 f(x) , dx$
(where $P_n(x)$ is a polynomial and f:[0,1]→R)
Can I say directly that
$lim_{nto {infty}}int_0^1 P_n(x)f(x) , dx$ =$int_0^1 f(x)f(x) , dx$
If not, is there a way to prove it?
polynomials definite-integrals
polynomials definite-integrals
asked Nov 22 at 2:20
kit kat
91
asked Nov 22 at 2:20
kit kat
91
asked Nov 22 at 2:20
kit kat
91
asked Nov 22 at 2:20
kit kat
91
asked Nov 22 at 2:20
kit kat
91
91
hint: $f$ is bounded and the convergence is uniform.
– Matematleta
Nov 22 at 2:23
1
Your title and your question are different.
– zhw.
Nov 22 at 3:54
add a comment |
hint: $f$ is bounded and the convergence is uniform.
– Matematleta
Nov 22 at 2:23
1
Your title and your question are different.
– zhw.
Nov 22 at 3:54
hint: $f$ is bounded and the convergence is uniform.
– Matematleta
Nov 22 at 2:23
hint: $f$ is bounded and the convergence is uniform.
– Matematleta
Nov 22 at 2:23
1
1
Your title and your question are different.
– zhw.
Nov 22 at 3:54
Your title and your question are different.
– zhw.
Nov 22 at 3:54
add a comment |
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hint: $f$ is bounded and the convergence is uniform.
– Matematleta
Nov 22 at 2:23
1
Your title and your question are different.
– zhw.
Nov 22 at 3:54