Finally, getting to the definition of the integral: let g be a simple measurable function on an m-measurable set E, where E = UNION(Ei), and g(x)=ai if x element of Ei. Then define the integral of g over E: INTEGRAL(E)(g) = SIGMAsubi(ai*m(…

"次の定理の証明を読んで混乱しました。 Theorem: If a function f is Riemann integrable over E, then it is also Lebesgue integrable and the Riemann integral equals the Lebesgue integral. In addition, the function f is continuous almost everyw…