User:Caliburn/s/mt/Definition:Weak Lp Quasinorm

Definition

Let $\struct {X, \Sigma, \mu}$ be a measure space and let $p \in \openint 0 \infty$.

Let $\map {L^{p, \infty} } {X, \Sigma, \mu}$ be the weak $L^p$ space on $\struct {X, \Sigma, \mu}$.

Let $F_f$ be the survival function of $f$.

Also see

• Equivalence of Definitions of Weak $L^p$ Quasinorm
• Weak $L^p$ Quasinorm is Well-Defined
• Weak $L^p$ Quasinorm is Quasinorm