  The concept of Rademacher type $p$ ($1\leq p\leq2$) plays an important role
in the local theory of Banach spaces. In \cite{mas88} Mascioni considers a
weakening of this concept and shows that for a Banach space $X$ weak Rademacher
type $p$ implies Rademacher type $r$ for all $r<p$.
  As with Rademacher type $p$ and weak Rademacher type $p$, we introduce the
concept of Haar type $p$ and weak Haar type $p$ by replacing the Rademacher
functions by the Haar functions in the respective definitions. We show that
weak Haar type $p$ implies Haar type $r$ for all $r<p$. This solves a problem
left open by Pisier \cite{pis75}.
  The method is to compare Haar type ideal norms related to different index
sets.
