积分、概率和分形测度

English | PDF | 1998 | 292 Pages | ISBN : 0387982051 | 24 MB

This book may be considered a continuation of my Springer-Verlag text Mea­ sure, Topology, and Fractal Geometry. It presupposes some elementary knowl­ edge of fractal geometry and the mathematics behind fractal geometry. Such knowledge might be obtained by study of Measure, Topology, and Fractal Ge­ ometry or by study of one of the other mathematically oriented texts (such as[13] or[87]). I hope this book will be appropriate to mathematics students at the beginning graduate level in the U.S. Most references are numbered and may be found at the end of the book; but Measure, Topology, and Fractal Geometry is referred to as[ MTFG]. One of the reviews of[MTFG] says that it "sacrific[es] breadth of coverage 1 for systematic development" -although I did not have it so clearly formulated as that in my mind at the time I was writing the book, I think that remark is exactly on target. That sacrifice has been made in this volume as well. In many cases, I do not include the most general or most complete form of a result. Sometimes I have only an example of an important development. The goal was to omit most material that is too tedious or that requires too much background.

这本书可以被认为是对我在Springer-Verlag出版的《测度、拓扑与分形几何》一书的延续。它假设读者对分形几何学及其背后的数学知识有一些基本了解。这些知识可以通过学习《测度、拓扑与分形几何》或阅读其他一些数学导向性书籍（比如[13]或[87]）获得。我希望这本书适合美国大学中一年级研究生水平的数学学生。书中所有引用都已编号，并且可以在书末找到；但《测度、拓扑与分形几何》一书则被标记为[MTFG]。《测度、拓扑与分形几何》一书的一条评论提到，该书“牺牲了覆盖范围的广度以换取系统性发展”——尽管在写作这本书的时候我并没有如此清晰地意识到这一点，在那时我的想法正是如此。我认为这条评论非常准确。这种牺牲也在本卷中进行了。在很多情况下，我没有包含一个结果的最一般形式或最完整的版本。有时，我会只举一个重要发展的例子。目标是排除大多数过于繁琐或者需要太多背景的知识材料。

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