Question about equality of Lebesgue integrals

[pangea429]

Please assist me with the following. I've been thinking about it for a while, but don't know where to begin.

Let g be a bounded measurable function on a measurable set A,
and h be bounded measurable functions on a measurable set B.

Suppose that $$\forall$$ c $$\in$$ R,

$$\mu$${x $$\in$$ A | g(x) $$\geq$$ c} = $$\mu$${x $$\in$$ B | h(x) $$\geq$$ c}.

Prove that $$\int$$_A g = $$\int$$_B h.

 

[pangea429]

There was a small typo, which I just corrected. The problem should make sense now.