There is one confusing moment. How did Rudin get (16)? My though is the following: Since $\dfrac{|B\mathbf{h}|}{|\mathbf{h}|}\to 0$ as $\mathbf{h}\to \mathbf{0}$. Fixing $\mathbf{h}\neq\mathbf{0}$ if $t\to 0$ then $t\mathbf{h}\to 0$. Hence $\dfrac{|B(t\mathbf{h})|}{|t\mathbf{h}|}\to 0$ by above.
Am I right? Any comment is greatly appreciated.
