Homework Statement
Let f be a positive integrable continuous function on ℝ. Fix a measurable set E such that E \subset [0,1]. Let
s = sup_{β \subset ℝ} [\int_{E} f_{β}(x)dx]
where
f_{β}(x) = f(x + β).
Show that s is actually a maximum (not just a supremum) that is, there is at...