diff --git a/Mathematics/2nd/Mathematical_analysis/Mathematical_analysis.tex b/Mathematics/2nd/Mathematical_analysis/Mathematical_analysis.tex index 167e1eb..049f65c 100644 --- a/Mathematics/2nd/Mathematical_analysis/Mathematical_analysis.tex +++ b/Mathematics/2nd/Mathematical_analysis/Mathematical_analysis.tex @@ -407,7 +407,7 @@ 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 $f$.