  The functional delta-method provides a convenient tool for deriving bootstrap
consistency of a sequence of plug-in estimators w.r.t. a given functional from
bootstrap consistency of the underlying sequence of estimators. It has recently
been shown in Beutner and Z\"ahle (2016) that the range of applications of the
functional delta-method for establishing bootstrap consistency in probability
of the sequence of plug-in estimators can be considerably enlarged by replacing
the usual condition of Hadamard differentiability of the given functional by
the weaker condition of quasi-Hadamard differentiability. Here we introduce the
notion of uniform quasi-Hadamard differentiability and show that this notion
extends the set of functionals for which almost sure bootstrap consistency of
the corresponding sequence of plug-in estimators can be obtained by the
functional delta-method. We illustrate the benefit of our results by means of
the Average Value at Risk functional as well as the composition of the Average
Value at Risk functional and the compound convolution functional. For the
latter we use a chain rule to be proved here. In our examples we consider the
weighted exchangeable bootstrap for independent observations and the blockwise
bootstrap for $\beta$-mixing observations.
