Two Nonequivalent Conditions for Weight Functions
Two Nonequivalent Conditions for Weight Functions
A nonnegative function on the real line satisfies the condition ${{\mathbf {A}}_\infty }$ if, given $\varepsilon > 0$, there exists a $\delta > 0$ such that if $I$ is an interval, $E \subset I$, and $|E| < \delta |I|$, then $\int _E {W \leq \varepsilon \int _I W }$. A …