Interactive Real Analysis

If f is a bounded function defined on a measurable set E with finite measure. Then f is integrable if the sets

E_k = { x E: (k-1) M / n ≤ f(x) < k M/n }

for k = -n, -(n-1), ... 0, 1, 2, ..., (n-1), n are measurable, then f is Lebesgue integrable.