Hint for the second part: you need $\mu$ to be semifinite so that for any $\epsilon &gt; 0$, there is a set $A$ with $0 &lt; \mu(A) &lt; \infty$ on which $|g(x)| &gt; \|g\|_\infty - \epsilon$.

Bound of norm of the operator $T(f)=fg$ on $L^p$ space
I am curious if anyone uses a skiing helmet for winter biking? Would this be safe? Are skiing helmets designed to protect you from the same kind of accidents that you would have on a bike?  

My thinking is that a ski helmet would:


Help to keep your ears warm
Would fit well with ski goggles (which fit poorly with my bike helmet)
Not have air vents in it which make you cold in the winter

