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Lebesque Integral

∫abf(x)dμ=∑i=1nyi⋅μ(Ayi)\int_{a}^{b} f(x) \mathrm{d} \mu=\sum_{i=1}^{n} y_{i} \cdot \mu\left(A_{y_{i}}\right)

and

∫abf(x)dμ=lim⁡n→∞∫abfn(x)dμ\int_{a}^{b} f(x) d \mu=\lim _{n \rightarrow \infty} \int_{a}^{b} f_{n}(x) d \mu
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