TY - BOOK ID - 8710709 TI - Radically elementary probability theory PY - 1987 SN - 0691084734 0691084742 1400882141 PB - Princeton Princeton University Press DB - UniCat KW - Martingales (Mathematics) KW - Stochastic processes. KW - Probabilities. KW - Martingales (Mathematics). KW - Stochastic processes KW - Probability KW - Statistical inference KW - Combinations KW - Mathematics KW - Chance KW - Least squares KW - Mathematical statistics KW - Risk KW - Random processes KW - Probabilities KW - Abraham Robinson. KW - Absolute value. KW - Addition. KW - Algebra of random variables. KW - Almost surely. KW - Axiom. KW - Axiomatic system. KW - Borel set. KW - Bounded function. KW - Cantor's diagonal argument. KW - Cardinality. KW - Cartesian product. KW - Central limit theorem. KW - Chebyshev's inequality. KW - Compact space. KW - Contradiction. KW - Convergence of random variables. KW - Corollary. KW - Correlation coefficient. KW - Counterexample. KW - Dimension (vector space). KW - Dimension. KW - Division by zero. KW - Elementary function. KW - Estimation. KW - Existential quantification. KW - Family of sets. KW - Finite set. KW - Hyperplane. KW - Idealization. KW - Independence (probability theory). KW - Indicator function. KW - Infinitesimal. KW - Internal set theory. KW - Joint probability distribution. KW - Law of large numbers. KW - Linear function. KW - Martingale (probability theory). KW - Mathematical induction. KW - Mathematician. KW - Mathematics. KW - Measure (mathematics). KW - N0. KW - Natural number. KW - Non-standard analysis. KW - Norm (mathematics). KW - Orthogonal complement. KW - Parameter. KW - Path space. KW - Predictable process. KW - Probability distribution. KW - Probability measure. KW - Probability space. KW - Probability theory. KW - Probability. KW - Product topology. KW - Projection (linear algebra). KW - Quadratic variation. KW - Random variable. KW - Real number. KW - Requirement. KW - Scientific notation. KW - Sequence. KW - Set (mathematics). KW - Significant figures. KW - Special case. KW - Standard deviation. KW - Statistical mechanics. KW - Stochastic process. KW - Subalgebra. KW - Subset. KW - Summation. KW - Theorem. KW - Theory. KW - Total variation. KW - Transfer principle. KW - Transfinite number. KW - Trigonometric functions. KW - Upper and lower bounds. KW - Variable (mathematics). KW - Variance. KW - Vector space. KW - W0. KW - Wiener process. KW - Without loss of generality. UR - https://www.unicat.be/uniCat?func=search&query=sysid:8710709 AB - Using only the very elementary framework of finite probability spaces, this book treats a number of topics in the modern theory of stochastic processes. This is made possible by using a small amount of Abraham Robinson's nonstandard analysis and not attempting to convert the results into conventional form. ER -