Convergence of Probability MeasuresJohn Wiley & Sons, 25 giu 2013 - 304 pagine A new look at weak-convergence methods in metric spaces-from a master of probability theory In this new edition, Patrick Billingsley updates his classic work Convergence of Probability Measures to reflect developments of the past thirty years. Widely known for his straightforward approach and reader-friendly style, Dr. Billingsley presents a clear, precise, up-to-date account of probability limit theory in metric spaces. He incorporates many examples and applications that illustrate the power and utility of this theory in a range of disciplines-from analysis and number theory to statistics, engineering, economics, and population biology. With an emphasis on the simplicity of the mathematics and smooth transitions between topics, the Second Edition boasts major revisions of the sections on dependent random variables as well as new sections on relative measure, on lacunary trigonometric series, and on the Poisson-Dirichlet distribution as a description of the long cycles in permutations and the large divisors of integers. Assuming only standard measure-theoretic probability and metric-space topology, Convergence of Probability Measures provides statisticians and mathematicians with basic tools of probability theory as well as a springboard to the "industrial-strength" literature available today. |
Dall'interno del libro
Risultati 1-5 di 27
Pagina
... dense subset consists of those points having only finitely many nonzero coordinates, each of them rational. If {x”} is fundamental, then each {1?} is fundamental and hence converges to some x,-, and of course x” converges to the point ...
... dense subset consists of those points having only finitely many nonzero coordinates, each of them rational. If {x”} is fundamental, then each {1?} is fundamental and hence converges to some x,-, and of course x” converges to the point ...
Pagina
... dense. Finally, by Baire's category theorem [M7], this implies that R°° is not o-compact. Let R? be the class of finite-dimensional sets, that is to say, the sets of the form 1r;1H for k 2 1 and H E R". Since 'lTk is continuous, it is ...
... dense. Finally, by Baire's category theorem [M7], this implies that R°° is not o-compact. Let R? be the class of finite-dimensional sets, that is to say, the sets of the form 1r;1H for k 2 1 and H E R". Since 'lTk is continuous, it is ...
Pagina
... dense and that C is not o-compact. For 0 s t1 < < tk s 1, define the natural projection from C to Rk by 'lTt1"'tk(X) = (x(t1), x(tk)). In C the finite-dimensional sets are those of the form Tray“ H, H E PK and they lie in C because the ...
... dense and that C is not o-compact. For 0 s t1 < < tk s 1, define the natural projection from C to Rk by 'lTt1"'tk(X) = (x(t1), x(tk)). In C the finite-dimensional sets are those of the form Tray“ H, H E PK and they lie in C because the ...
Pagina
... dense, then Ac = but the converse is false. Find an A that is everywhere dense even though _4° : 0. 1.17. Every locally compact subset of C is nowhere dense. 1.18. In connection with Example 1.3, consider the space Cb(T) of bounded ...
... dense, then Ac = but the converse is false. Find an A that is everywhere dense even though _4° : 0. 1.17. Every locally compact subset of C is nowhere dense. 1.18. In connection with Example 1.3, consider the space Cb(T) of bounded ...
Pagina
... dense. Let AP be the class of rectangles such that each coordinate of each vertex lies in D. If A 6 AP, then, since 8Q, C U,' [1): y, follows by inclusion-exclusion that PnA —> PA. From this and the fact that D is dense, it follows that ...
... dense. Let AP be the class of rectangles such that each coordinate of each vertex lies in D. If A 6 AP, then, since 8Q, C U,' [1): y, follows by inclusion-exclusion that PnA —> PA. From this and the fact that D is dense, it follows that ...
Sommario
THE SPACE C | ix |
THE SPACE D | viii |
DEPENDENT VARIABLES | xlviii |
OTHER MODES OF CONVERGENCE | lxiii |
APPENDIX_M | 16 |
INDEX | 38 |
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