I am thinking about the relation between the VC-dimension and the pseudo-dimension, and confused about them.
Let $H$ be a family of real-valued functions. We can define a function $c(h,t):x\rightarrow 1_{h(x)>t}$ for $h\in H$ and $t\ge 0$. Based on $c(h,t)$, we define another family of functions $C$ as follows, \begin{align} C=\{c(h,t) :h\in H, t\ge 0 \}. \end{align}
Is VC dimension of $C$ is equal to the pseudo dimension of $H$? How can we prove this?
