I have trouble solving this problem for few hours...
- For (a), I was just trying with the range of integration by $\int_a^b$ where a,b is large enough. Since h(b)-h(a) $\leq \int^b_a H(t) \rightarrow 0$, it is concluded that h has limit in inf (Cauchy seq). Then h(t) should be zero by assumption.
Is it clear? or is there another way to make this proof more neatly?
+I think the inequality part in my proof does not make sense as it is not accompanied with $||$, (absolute value).
- For (b) and (c), my idea was MVT, and integration by parts... but I couldn't make it.