Abraham Wald's paper discusses the foundations of a general theory of statistical decision functions, including both classical non-sequential and sequential cases. The author revisits the assumptions made in his previous work [3], which he finds to be unnecessarily restrictive. In this paper, he derives main results from weaker conditions that are more commonly satisfied in statistical problems. The compactness condition for the space of admissible distribution functions is relaxed, and the continuity assumption on the weight function is dropped, allowing for simplified weight functions that take only the values 0 and 1. The paper also introduces new results, such as the existence of minimax solutions under weaker conditions. The theory is developed from the beginning, with basic definitions restated for clarity. The paper is divided into three sections: the first section covers zero-sum two-person games, the second section treats discrete chance variables, and the third section deals with continuous cases. The author shows that the statistical decision problem can be interpreted as a zero-sum game, and he proves that the game is strictly determined under certain conditions.Abraham Wald's paper discusses the foundations of a general theory of statistical decision functions, including both classical non-sequential and sequential cases. The author revisits the assumptions made in his previous work [3], which he finds to be unnecessarily restrictive. In this paper, he derives main results from weaker conditions that are more commonly satisfied in statistical problems. The compactness condition for the space of admissible distribution functions is relaxed, and the continuity assumption on the weight function is dropped, allowing for simplified weight functions that take only the values 0 and 1. The paper also introduces new results, such as the existence of minimax solutions under weaker conditions. The theory is developed from the beginning, with basic definitions restated for clarity. The paper is divided into three sections: the first section covers zero-sum two-person games, the second section treats discrete chance variables, and the third section deals with continuous cases. The author shows that the statistical decision problem can be interpreted as a zero-sum game, and he proves that the game is strictly determined under certain conditions.