DLMF:1.7.E6 (Q247): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3abdec

Revision as of 16:02, 1 January 2020

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English
DLMF:1.7.E6
No description defined

    Statements

    Defining formula
    ( ∫ a b ( f ⁢ ( x ) + g ⁢ ( x ) ) p ⁢ d x ) 1 / p ≤ ( ∫ a b ( f ⁢ ( x ) ) p ⁢ d x ) 1 / p + ( ∫ a b ( g ⁢ ( x ) ) p ⁢ d x ) 1 / p . superscript superscript subscript 𝑎 𝑏 superscript 𝑓 𝑥 𝑔 𝑥 𝑝 𝑥 1 𝑝 superscript superscript subscript 𝑎 𝑏 superscript 𝑓 𝑥 𝑝 𝑥 1 𝑝 superscript superscript subscript 𝑎 𝑏 superscript 𝑔 𝑥 𝑝 𝑥 1 𝑝 {\displaystyle{\displaystyle\left(\int_{a}^{b}(f(x)+g(x))^{p}\mathrm{d}x\right% )^{1/p}\leq\left(\int_{a}^{b}(f(x))^{p}\mathrm{d}x\right)^{1/p}+\left(\int_{a}% ^{b}(g(x))^{p}\mathrm{d}x\right)^{1/p}.}}
    0 references
    DLMF id
    DLMF:1.7.E6
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
     
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