Exact capacity results for stable processes (Q1271259)

The author establishes a formula for the probability that a drift-free subordinator hits a given interval, a subordinator being an increasing Lévy process taking real values. The main result is that if \(T_{\alpha}\) \((0 <\alpha < 1)\) is a stable subordinator of index \(\alpha\) and \(B\) an analytic subset of \(\mathbb R_+\), then \(\{ \text{cap}_{\theta} [T_{\alpha}(B)] > 0 \}\) satisfies a zero-one law (\( \text{cap}_{\theta}(B)\) is the capacity with respect to the Riesz kernel of order \(\theta\)).