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Lemma 4.7 .
Suppose φ \varphi ψ \psi φ 1 , … , φ n \varphi_{1},\dots,\varphi_{n} ω \omega − M ≤ φ ≤ ψ ≤ 0 -M\leq\varphi\leq\psi\leq 0 − M ≤ u i ≤ 0 -M\leq u_{i}\leq 0 M ≥ 1 M\geq 1
0 ≤ ∫ ( ψ − φ ) MA ( φ 1 , … , φ n ) ≤ 4 M ( ∫ ( ψ − φ ) MA ( φ 2 ) ) 1 2 n . 0\leq\int(\psi-\varphi)\MA(\varphi_{1},\dots,\varphi_{n})\leq 4M\left(\int(\psi-\varphi)\MA(\frac{\varphi}{2})\right)^{\frac{1}{2^{n}}}.