The paper considers classes of decision procedures which in certain ways put a bound on the associated losses of incorrect terminal decision or cost of experimentation. Conditions are given under which these classes fulfill the conditions that Wald imposes on classes of decision procedures in his general theory.
H. S. Konijn. "On Certain Classes of Statistical Decision Procedures." Ann. Math. Statist. 24 (3) 440 - 448, September, 1953. https://doi.org/10.1214/aoms/1177728983