Assertion A(p) . [01A3] Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.
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Assertion A(p) .
To any p p -tuple φ 1 , … , φ p \varphi_{1},\dots,\varphi_{p} of bounded θ \theta -psh
functions is associated a positive Radon measure M ( φ 1 , … , φ p ) \MAC(\varphi_{1},\dots,\varphi_{p}) of mass { θ } n \{\theta\}^{n}
such that:
•
if φ 1 , … , φ p \varphi_{1},\dots,\varphi_{p} are model functions then
(3.2)
M ( φ 1 , … , φ p ) = ( θ + d d c φ 1 ) ∧ ⋯ ∧ ( θ + d d c φ p ) ∧ ( θ + d d c φ p + 1 ′ ) ∧ ⋯ ∧ ( θ + d d c φ n ′ ) \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})
•
the mapping
( ψ , φ 1 , … , φ p ) ↦ ∫ ψ M ( φ 1 , … , φ p ) (\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.