ScalingStacks

Assertion A(p) . [01A3]

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Assertion A(p).

To any pp-tuple φ1,…,φp\varphi_{1},\dots,\varphi_{p} of bounded θ\theta-psh functions is associated a positive Radon measure M⁡(φ1,…,φp)\MAC(\varphi_{1},\dots,\varphi_{p}) of mass {θ}n\{\theta\}^{n} such that:

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    if φ1,…,φp\varphi_{1},\dots,\varphi_{p} are model functions then

    (3.2) M⁡(φ1,…,φp)=(θ+d​dc​φ1)∧⋯∧(θ+d​dc​φp)∧(θ+d​dc​φp+1′)∧⋯∧(θ+d​dc​φn′)\MAC(\varphi_{1},\dots,\varphi_{p})=(\theta+dd^{c}\varphi_{1})\wedge\dots\wedge(\theta+dd^{c}\varphi_{p})\wedge(\theta+dd^{c}\varphi_{p+1}^{\prime})\wedge\dots\wedge(\theta+dd^{c}\varphi_{n}^{\prime})
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    the mapping

    (ψ,φ1,…,φp)↦∫ψ​M⁡(φ1,…,φp)(\psi,\varphi_{1},\dots,\varphi_{p})\mapsto\int\psi\MAC(\varphi_{1},\dots,\varphi_{p})

    is continuous along decreasing nets of bounded θ\theta-psh functions.

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