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corrected mathematical analysis
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victorballester7 committed Jun 24, 2023
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Let $f:\RR \rightarrow\CC $ be a $T$-periodic function. Then: $$\int_a^{a+T}f(x)\dd{x}=\int_0^Tf(x)\dd{x}$$ where $a\in\RR $. In particular, $$\int_a^{a+kT}f(x)\dd{x}=k\int_0^Tf(x)\dd{x}$$
\end{proposition}
\begin{lemma}\label{MA:periodicbounded}
Let $f:\RR \rightarrow\CC $ be a $T$-periodic continuous function. Then, $|f|$ is bounded.
Let $f:\RR \rightarrow\CC $ be a $T$-periodic continuous function. Then, $\abs{f}$ is bounded.
\end{lemma}
\begin{sproof}
Use \mnameref{RVF:weierstrass} on the interval $[0,T]$ and the periodicity of $f$.
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