Weak type with a normed domain
= Weak type with a normed domain
{title2=$\lambda\{|Tf|>a\}\leq(C\|f\|_E/a)^q$}
For a <normed space> $E$ and $0<q<\infty$, an operator $T:E\to L^0$ is of weak type $(E,q)$ when the displayed distribution bound holds uniformly over $f\in E$ and $a>0$. No completeness of $E$ is needed. A <sublinear operator> has pointwise triangle domination and absolute homogeneity; its outputs may be understood modulo <almost everywhere> equality.