ScalingStacks

7.2. Equicontinuity [01GT]

Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.

Complete original source context · Original author HTML

7.2. Equicontinuity

The Lipschitz estimates in Theorem 6.1 carry over to general θ\theta-psh functions. As a consequence we have

Corollary 7.7.

For any SNC model on which θ\theta is determined, the family

{φ∘emb𝒳∣φ∈PSH⁡(X,θ)}\{\varphi\circ\emb_{\mathcal{X}}\mid\varphi\in\PSH(X,\theta)\}

is an equicontinuous family of functions on Δ𝒳\Delta_{\mathcal{X}}.

Original mathematics by the credited authors. Source-backed reader collection; mathematical self-containment is not assessed.