User:Caliburn/s/mt/LpStuff

• User:Caliburn/s/mt/Definition:Lp Space
  • User:Caliburn/s/mt/Definition:Lp Space/Lp Norm
    • User:Caliburn/s/mt/Lp Norm is Well-Defined
    • User:Caliburn/s/mt/Lp Norm is Norm
  • User:Caliburn/s/mt/Definition:Lp Space/L-Infinity Norm
    • User:Caliburn/s/mt/L-Infinity Norm is Well-Defined
    • User:Caliburn/s/mt/L-Infinity Norm is Norm
  • User:Caliburn/s/mt/Definition:Lp Space/Vector Space
    • User:Caliburn/s/mt/Lp Space is Subset of Space of Measurable Functions Identified by A.E. Equality - technical quibble, we need to show that the $\sim_\mu$-equivalence class of a function in ${\mathcal L}^p$ contains only other elements of ${\mathcal L}^p$ so it doesn't get bigger when we expand the ambient space. This just means I can restrict all the operations nicely.
    • User:Caliburn/s/mt/Lp Space is Vector Space
  • User:Caliburn/s/mt/Definition:Lp Space/Normed Vector Space
• User:Caliburn/s/mt/Definition:Integral on L-1 Space

Weak

• User:Caliburn/s/mt/Definition:Weak Lp Space
  • User:Caliburn/s/mt/Definition:Weak Lp Space/Quasinormed Vector Space
• User:Caliburn/s/mt/Weak Lp Space is Vector Space
• User:Caliburn/s/mt/Definition:Weak Lp Quasinorm
• User:Caliburn/s/mt/Weak Lp Quasinorm is Quasinorm
• User:Caliburn/s/mt/Lp Space Contained in Weak Lp Space