What is the meaning of "$f$g has constant sign a.e." for question 4 on page 143 of Wheeden & Zygmund's Measure and Integral?
2026-04-29 04:57:44.1777438664
What is the meaning of "$fg$ has constant sign a.e."?
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It means that $fg$ is either positive a.e., or negative a.e..
(In other words, either the complement of the set $\{x\in X: fg(x)>0\}$ has measure zero, or the complement of the set $\{x\in X:fg(x)<0\}$ has measure zero.)