Under certain continuity conditions, we estimate upper and lower box dimensions of the graph of a function defined on the Sierpiński gasket. We also give an upper bound for Hausdorff dimension and box dimension of the graph of a function having finite energy. Further, we introduce two sets of definitions of bounded variation for a function defined on the Sierpiński gasket. We show that fractal dimension of the graph of a continuous function of bounded variation is $\frac{log3}{log2}.$ 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 $\frac{log3}{log2}$-dimensional Hausdorff measure.

在某些连续性条件下，我们估计了在 Sierpiński 垫片上定义的函数图的上下框尺寸。我们还给出了具有有限能量的函数图的 Hausdorff 维数和盒维数的上限。此外，我们为在 Sierpiński 垫片上定义的函数引入了两组有界变化定义。我们证明了有界变化的连续函数图的分形维数是$\frac{日志3}{日志2}.$我们还证明了所有有界变分函数的类在算术运算下都是封闭的。此外，我们证明了每个有界变分函数几乎在任何地方都是连续的$\frac{日志3}{日志2}$维豪斯多夫测度。