My question is above. Firstly, I don't actually know whether it is true or not (!). Secondly, if I were to try to prove it, then I have very little idea how to. The potential steps that I have always done are steps from a constant level to another constant level (Heavyside), whereas this is different.
I would imagine the answer is yes, but I'm not sure how to show it.
Can I approximate the curve by small steps (/sums of Heavyside functions), and then show that a larger Heavyside step gives a larger probability?