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“Decision Systems and Nonstochastic Randomness” presents the first mathematical formalization of the statistical regularities of non-stochastic randomness and demonstrates how these regularities extend the standard probability-based model of decision making under uncertainty, allowing for the description of uncertain mass events that do not fit standard stochastic models. Each self-contained chapter of this neatly-structured monograph includes a detailed introduction and summary of its contents. The included results are presented not only with rigorous proofs but also through numerous intuitive examples. An appendix is provided which includes classic results from the theory of functions and measured sets as well as decision theory, offering an overview of the necessary prerequisites. The formalism of statistical regularities developed in this book will have a significant influence on decision theory and information theory as well as numerous other disciplines. Because of these far-reaching implications, this book may be a useful resource for statisticians, mathematicians, engineers, economists and other utilizing nonstochastic modeling and decision theory.

Random data (Statistics). --- Random dynamical systems. --- Statistical decision. --- Statistical decision --- Random data (Statistics) --- Random dynamical systems --- Mathematics --- Mathematical Statistics --- Physical Sciences & Mathematics --- Dynamical systems, Random --- Data, Random (Statistics) --- Decision problems --- Mathematics. --- Operations research. --- Decision making. --- Business mathematics. --- Applied mathematics. --- Engineering mathematics. --- Game theory. --- Probabilities. --- Statistics. --- Probability Theory and Stochastic Processes. --- Applications of Mathematics. --- Business Mathematics. --- Statistical Theory and Methods. --- Game Theory, Economics, Social and Behav. Sciences. --- Operation Research/Decision Theory. --- Differentiable dynamical systems --- Statistics --- Stochastic processes --- Game theory --- Operations research --- Management science --- Distribution (Probability theory. --- Mathematical statistics. --- Operations Research/Decision Theory. --- Operational analysis --- Operational research --- Industrial engineering --- Research --- System theory --- Statistical inference --- Statistics, Mathematical --- Probabilities --- Sampling (Statistics) --- Arithmetic, Commercial --- Business --- Business arithmetic --- Business math --- Commercial arithmetic --- Finance --- Math --- Science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Statistical methods --- Statistics . --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Games, Theory of --- Theory of games --- Mathematical models --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Engineering --- Engineering analysis --- Mathematical analysis --- Probability --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Decision making