**MSC:**- 62F05 Asymptotic properties of tests
- 62F12 Asymptotic properties of estimators

experiment $E$. One of the basic objectives of asymptotic decision theory

is to derive asymptotically ``best`` decisions in $E_n$ from optimal

decisions in the limit experiment $E$. A central statement in this

context is the Hajek-LeCam bound which represents a lower bound for the

maximum risk of a sequence of decisions.

It is given a simplified proof for the existence of accumulation points

of a sequence of generalized decisions functions using the

$\varepsilon$-Blackwell sufficiency of sufficient statistics defined

on finite experiments. That is the main step for deriving the Hajek-LeCam

bound for weakly convergent sequences of experiments.