update notations and fix typos
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@@ -53,7 +53,7 @@ $$
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Since $\epsilon$ is arbitrary, $h\in \mathscr{R}(\alpha)$ on $[a, b]$.
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EOP
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QED
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### Properties of Integrable Functions
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@@ -108,4 +108,4 @@ So $U(P,h,\alpha)\leq U(P,f,\alpha)+U(P,g,\alpha)\leq \int_a^b f d\alpha + \int_
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Since $\epsilon$ is arbitrary, $\int_a^b h d\alpha \leq \int_a^b f d\alpha + \int_a^b g d\alpha$.
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EOP
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QED
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