<p><strong>The best introduction to probability and measure!!!!</strong></p><p><b><font size="6">Probability & Measure Theory, Second Edition <!--Element not supported - Type: 8 Name: #comment--><br/></font>by <a href="http://www.amazon.com/exec/obidos/search-handle-url/104-8650272-2332702?%5Fencoding=UTF8&search-type=ss&index=books&field-author=Robert%20B.%20Ash">Robert B. Ash</a> (Author), <a href="http://www.amazon.com/exec/obidos/search-handle-url/104-8650272-2332702?%5Fencoding=UTF8&search-type=ss&index=books&field-author=Catherine%20A.%20Doleans-Dade">Catherine A. Doleans-Dade</a> (Author) </b></p><p><b><span class="tiny"><strong>Key Phrases: </strong><a href="http://www.amazon.com/phrase/same-positive-type/ref=sip_top_0/104-8650272-2332702">same positive type</a>, <a href="http://www.amazon.com/phrase/measurable-cylinders/ref=sip_top_1/104-8650272-2332702">measurable cylinders</a>, <a href="http://www.amazon.com/phrase/product-measure-theorem/ref=sip_top_2/104-8650272-2332702">product measure theorem</a>, <a href="http://www.amazon.com/phrase/Problems-Let/ref=cap_top_0/104-8650272-2332702">Problems Let</a> (<a href="http://www.amazon.com/Probability-Measure-Theory-Robert-Ash/dp/0120652021#sipbody">more...</a>)</span></b></p><li><b>Hardcover:</b> 516 pages</li><li><b>Publisher:</b> Academic Press; 2 edition (December 6, 1999)</li><p><td width="0" valign="top" align="right"></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td>The book very nicely develops the basics of measure theory from a probability perspective (e.g. includes Caratheodory extension theorem, Lebesgue-Stieltjes measures, weak convergence and Kolmogorov extension theorem). It then gives a brief introduction to functional analysis and proceeds to probability theory, martingales and concludes with brownian motion and stochastic integration. <br/><br/>All standard results are given and the book is self-contained. It is a concise, yet readable introduction to this area (less concise then Rudin, Williams but more than Billingsly). An excellent feature of this book is that full solutions to some of the exercises are provided at the end. This makes this book ideal for self-study. The only prerequisite for this book is elementary real analysis (say chapters 1-7 of Rudin's principles of mathematical analysis). <br/><br/>There are other excellent books on measure theory (Rudin, Royden), but if you are interested in measure theory from a probabilistic view this is the book to choose. <br/></p><p>As far as a probability textbook, it is clearer and more readable than Billingsly, Chung, Williams and Durrett.<td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></p>

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