Extensions and Shadows (10)

Continuing our proof of Lemma A.4 and Corollary A.5 of Paper S5. It’s straightforward to check that \( g(\alpha) \) monotonically increases in \( \alpha \) strictly. The last line holds because \( g(0)=1 \) and \( g(y)=(1-t)^{-k} \). Thus, \[ (3.3) \qquad \int_0^y g(\alpha) d\alpha + 1 – \left( 1-t \right)^{-k} < U_k < […]