Does this norm have a specific name? References?
$begingroup$
Let $(X,mathscr{B},mu)$ be a $sigma$-finite measure space. Let $gamma$ be a probability measure on $L_2(mu)$ with $mathrm{supp} , gamma = L_2(mu)$ and existing first moment. Then
$$
f mapsto |f| := int |langle f,grangle|,gamma(mathrm{d}g)
$$
is a norm on $L_2(mu).$ Does this norm have a name? Can anyone give me some references where such normed vector spaces were studied?
functional-analysis reference-request norm lp-spaces
edited Dec 29 '18 at 21:42
Theo Bendit
17.1k12149
asked Dec 29 '18 at 21:39
H17H17
313
$endgroup$
add a comment |
$begingroup$
Let $(X,mathscr{B},mu)$ be a $sigma$-finite measure space. Let $gamma$ be a probability measure on $L_2(mu)$ with $mathrm{supp} , gamma = L_2(mu)$ and existing first moment. Then
$$
f mapsto |f| := int |langle f,grangle|,gamma(mathrm{d}g)
$$
is a norm on $L_2(mu).$ Does this norm have a name? Can anyone give me some references where such normed vector spaces were studied?
functional-analysis reference-request norm lp-spaces
edited Dec 29 '18 at 21:42
Theo Bendit
17.1k12149
asked Dec 29 '18 at 21:39
H17H17
313
$endgroup$
add a comment |
$begingroup$
Let $(X,mathscr{B},mu)$ be a $sigma$-finite measure space. Let $gamma$ be a probability measure on $L_2(mu)$ with $mathrm{supp} , gamma = L_2(mu)$ and existing first moment. Then
$$
f mapsto |f| := int |langle f,grangle|,gamma(mathrm{d}g)
$$
is a norm on $L_2(mu).$ Does this norm have a name? Can anyone give me some references where such normed vector spaces were studied?
functional-analysis reference-request norm lp-spaces
edited Dec 29 '18 at 21:42
Theo Bendit
17.1k12149
asked Dec 29 '18 at 21:39
H17H17
313
$endgroup$
Let $(X,mathscr{B},mu)$ be a $sigma$-finite measure space. Let $gamma$ be a probability measure on $L_2(mu)$ with $mathrm{supp} , gamma = L_2(mu)$ and existing first moment. Then
$$
f mapsto |f| := int |langle f,grangle|,gamma(mathrm{d}g)
$$
is a norm on $L_2(mu).$ Does this norm have a name? Can anyone give me some references where such normed vector spaces were studied?
functional-analysis reference-request norm lp-spaces
functional-analysis reference-request norm lp-spaces
edited Dec 29 '18 at 21:42
Theo Bendit
17.1k12149
asked Dec 29 '18 at 21:39
H17H17
313
edited Dec 29 '18 at 21:42
Theo Bendit
17.1k12149
asked Dec 29 '18 at 21:39
H17H17
313
edited Dec 29 '18 at 21:42
Theo Bendit
17.1k12149
edited Dec 29 '18 at 21:42
Theo Bendit
17.1k12149
edited Dec 29 '18 at 21:42
Theo Bendit
17.1k12149
17.1k12149
asked Dec 29 '18 at 21:39
H17H17
313
asked Dec 29 '18 at 21:39
H17H17
313
asked Dec 29 '18 at 21:39
H17H17
313
313
add a comment |
add a comment |
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