 Fractional uniform cover

Nonnegative weights ${\lambda }_A$ on coordinate subsets form a fractional uniform cover when the displayed equality holds for each coordinate. Rational weights can be multiplied by a common denominator to become an integer uniform cover. The uniform covers theorem then gives $\log |S|\le {\sum }_A{\lambda }_A\log |S_A|$. Exact equality of coordinate coverage matters when projection measures may be less than one.