Vector-valued ergodic theorems for multiparameter additive processes
Ryotaro Sato (1999)
Colloquium Mathematicae
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Let X be a reflexive Banach space and (Ω,Σ,μ) be a σ-finite measure space. Let d ≥ 1 be an integer and T=T(u):u=(, ... ,, ≥ 0, 1 ≤ i ≤ d be a strongly measurable d-parameter semigroup of linear contractions on ((Ω,Σ,μ);X). We assume that to each T(u) there corresponds a positive linear contraction P(u) defined on ((Ω,Σ,μ);ℝ) with the property that ∥ T(u)f(ω)∥ ≤ P(u)∥f(·)∥(ω) almost everywhere on Ω for all f ∈ ((Ω,Σ,μ);X). We then prove stochastic and pointwise ergodic theorems...