Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.
Source coverage notes 1 original structured objects have an unresolved mathematical role; their permanent tags identify source occurrences only. Complete original source context · Original author HTML
Lemma 3.4 .
Let ψ \psi χ i ≥ φ i \chi_{i}\geq\varphi_{i} i = 1 , … , p i=1,\dots,p θ \theta
∫ ψ M ( χ 1 , … , χ p ) \displaystyle\int\psi\MAC(\chi_{1},\dots,\chi_{p}) ≥ ∫ ψ M ( φ 1 , … , φ p ) \displaystyle\geq\int\psi\MAC(\varphi_{1},\dots,\varphi_{p})
+ ∑ i = 1 p ∫ ( φ i − χ i ) M ( φ 1 , … , φ i − 1 , 0 , χ i + 1 , … , χ p ) . \displaystyle+\sum_{i=1}^{p}\int(\varphi_{i}-\chi_{i})\MAC(\varphi_{1},\dots,\varphi_{i-1},0,\chi_{i+1},\dots,\chi_{p}).