论文标题
Sierpinski垫圈的有界变化
Bounded Variation on the Sierpinski Gasket
论文作者
论文摘要
在某些连续性条件下，我们估计了Sierpinski垫圈上定义的函数的图形上和下盒尺寸。我们还为具有有限能量的功能的函数图的Hausdorff尺寸和框尺寸提供了上限。此外，我们介绍了在Sierpinski垫圈上定义的函数的有界变化的两组定义。我们表明，有界变化的连续函数的图形的分形维是log 3/log 2。我们还证明，在算术操作下，所有有界变异函数的类都封闭。此外，我们表明，在log 3/log 2尺寸的Hausdorff测量的意义上，有界变化的每个函数几乎是连续的。
Under certain continuity conditions, we estimate upper and lower box dimension of graph of a function defined on the Sierpinski gasket. We also give an upper bound for Hausdorff dimension and box dimension of graph of function having finite energy. Further, we introduce two sets of definitions of bounded variation for a function defined on the Sierpinski gasket. We show that fractal dimension of graph of a continuous function of bounded variation is log 3/log 2. We also prove that the class of all bounded variation functions is closed under arithmetic operations. Furthermore, we show that every function of bounded variation is continuous almost everywhere in the sense of log 3/log 2 dimensional Hausdorff measure.
