论文标题
关于库苏卡措施的另一个观点
Another point of view on Kusuoka's measure
论文作者
论文摘要
Kusuoka对分形的度量是一种非常特殊的吉布斯度量，因为其潜力是不连续的，而Gibbs测量的标准理论则需要连续（Actually，Hölder）电位。在本文中，我们将看到，对于许多分形，可以在标准理论的范围内完全构建一类矩阵值的吉布斯措施。自然会有一些较小的修改，但它们仅是由于我们正在处理矩阵值的功能和度量。我们将使用这些矩阵值吉布斯的措施来建立分形上的自相似的迪里奇形式。此外，我们将看到Kusuoka的措施可以从基质值吉布斯度量中以简单的方式恢复。
Kusuoka's measure on fractals is a Gibbs measure of a very special kind, because its potential is discontinuous, while the standard theory of Gibbs measures requires continuous (actuallly, Hölder) potentials. In this paper, we shall see that for many fractals it is possible to build a class of matrix-valued Gibbs measures completely within the scope of the standard theory; there are naturally some minor modifications, but they are only due to the fact that we are dealing with matrix-valued functions and measures. We shall use these matrix-valued Gibbs measures to build self-similar Dirichlet forms on fractals. Moreover, we shall see that Kusuoka's measure can be recovered in a simple way from the matrix-valued Gibbs measure.
