diff options
Diffstat (limited to 'fvv2/n1.lyx')
| -rw-r--r-- | fvv2/n1.lyx | 52 |
1 files changed, 26 insertions, 26 deletions
diff --git a/fvv2/n1.lyx b/fvv2/n1.lyx index e7eda47..fee5af0 100644 --- a/fvv2/n1.lyx +++ b/fvv2/n1.lyx @@ -128,7 +128,7 @@ integral indefinida \end_inset con -\begin_inset Formula $F(x):=\int_{a}^{x}f$ +\begin_inset Formula $F(x)\coloneqq \int_{a}^{x}f$ \end_inset . @@ -243,7 +243,7 @@ rectángulo \end_inset -dimensional -\begin_inset Formula $R:=[a_{1},b_{1}]\times\dots\times[a_{n},b_{n}]\subset\mathbb{R}^{n}$ +\begin_inset Formula $R\coloneqq [a_{1},b_{1}]\times\dots\times[a_{n},b_{n}]\subset\mathbb{R}^{n}$ \end_inset se define como @@ -308,7 +308,7 @@ Una partición \series default sobre este rectángulo es una lista -\begin_inset Formula $P:=(P_{1},\dots,P_{n})$ +\begin_inset Formula $P\coloneqq (P_{1},\dots,P_{n})$ \end_inset en la que cada @@ -361,7 +361,7 @@ Si \end_inset es acotada y -\begin_inset Formula $P:=(P_{i})_{i=1}^{n}$ +\begin_inset Formula $P\coloneqq (P_{i})_{i=1}^{n}$ \end_inset es una partición de @@ -377,7 +377,7 @@ Si \end_inset denotamos -\begin_inset Formula $m_{S_{h}}(f):=\inf\{f(x)\}_{x\in S_{h}}$ +\begin_inset Formula $m_{S_{h}}(f)\coloneqq \inf\{f(x)\}_{x\in S_{h}}$ \end_inset y @@ -1251,7 +1251,7 @@ La función \end_inset dada por -\begin_inset Formula $f(0.c_{1}c_{2}\cdots c_{n}\cdots_{(3)}):=0.\frac{c_{1}}{2}\frac{c_{2}}{2}\cdots\frac{c_{n}}{2}\cdots_{(2)}$ +\begin_inset Formula $f(0.c_{1}c_{2}\cdots c_{n}\cdots_{(3)})\coloneqq 0.\frac{c_{1}}{2}\frac{c_{2}}{2}\cdots\frac{c_{n}}{2}\cdots_{(2)}$ \end_inset es suprayectiva, luego @@ -1452,7 +1452,7 @@ Sea \end_inset , -\begin_inset Formula $B:=\{x\in A\mid \text{osc}(f,x)\geq\varepsilon\}$ +\begin_inset Formula $B\coloneqq \{x\in A\mid \text{osc}(f,x)\geq\varepsilon\}$ \end_inset es cerrado. @@ -1539,7 +1539,7 @@ teorema de Lebesgue de caracterización de las funciones integrables \end_inset si y sólo si -\begin_inset Formula $B:=\{x\in R\mid f\text{ no es continua en }x\}$ +\begin_inset Formula $B\coloneqq \{x\in R\mid f\text{ no es continua en }x\}$ \end_inset tiene medida nula. @@ -1559,7 +1559,7 @@ status open \end_inset Sea -\begin_inset Formula $B_{k}:=\{x\in R\mid o(f,x)\geq\frac{1}{k}\}$ +\begin_inset Formula $B_{k}\coloneqq \{x\in R\mid o(f,x)\geq\frac{1}{k}\}$ \end_inset , basta probar que cada @@ -1671,7 +1671,7 @@ Fijado . Es claro que -\begin_inset Formula $C:=R\backslash\bigcup_{k}N_{k}$ +\begin_inset Formula $C\coloneqq R\backslash\bigcup_{k}N_{k}$ \end_inset es compacto, y como para cada @@ -1868,15 +1868,15 @@ Sean \end_inset como -\begin_inset Formula $lf_{x}(y):=f(x,y)$ +\begin_inset Formula $lf_{x}(y)\coloneqq f(x,y)$ \end_inset , -\begin_inset Formula $s_{lf}(x):=\underline{\int_{R_{2}}}lf_{x}(y_{1},\dots,y_{m})dy_{1}\cdots dy_{m}$ +\begin_inset Formula $s_{lf}(x)\coloneqq \underline{\int_{R_{2}}}lf_{x}(y_{1},\dots,y_{m})dy_{1}\cdots dy_{m}$ \end_inset y -\begin_inset Formula $S_{lf}(x):=\overline{\int_{R_{2}}}lf_{x}(y_{1},\dots,y_{m})dy_{1}\cdots dy_{m}$ +\begin_inset Formula $S_{lf}(x)\coloneqq \overline{\int_{R_{2}}}lf_{x}(y_{1},\dots,y_{m})dy_{1}\cdots dy_{m}$ \end_inset , y para cada @@ -1884,15 +1884,15 @@ Sean \end_inset definimos -\begin_inset Formula $rf_{y}(x):=f(x,y)$ +\begin_inset Formula $rf_{y}(x)\coloneqq f(x,y)$ \end_inset , -\begin_inset Formula $s_{rf}(y):=\int_{R_{1}}rf_{y}(x_{1},\dots,x_{n})dx_{1}\cdots dx_{m}$ +\begin_inset Formula $s_{rf}(y)\coloneqq \int_{R_{1}}rf_{y}(x_{1},\dots,x_{n})dx_{1}\cdots dx_{m}$ \end_inset y -\begin_inset Formula $S_{rf}(y):=\overline{\int_{R_{1}}}rf_{y}(x_{1},\dots,x_{n})dx_{1}\cdots dx_{m}$ +\begin_inset Formula $S_{rf}(y)\coloneqq \overline{\int_{R_{1}}}rf_{y}(x_{1},\dots,x_{n})dx_{1}\cdots dx_{m}$ \end_inset . @@ -1944,11 +1944,11 @@ En la práctica esto significa que \end_inset donde -\begin_inset Formula $d\vec{x}:=dx_{1}\cdots dx_{n}$ +\begin_inset Formula $d\vec{x}\coloneqq dx_{1}\cdots dx_{n}$ \end_inset y -\begin_inset Formula $d\vec{y}:=dy_{1}\cdots dy_{m}$ +\begin_inset Formula $d\vec{y}\coloneqq dy_{1}\cdots dy_{m}$ \end_inset . @@ -2408,7 +2408,7 @@ Funciones que contienen \begin_layout Standard Llamamos -\begin_inset Formula $d:=\frac{ac-b^{2}}{a}$ +\begin_inset Formula $d\coloneqq \frac{ac-b^{2}}{a}$ \end_inset y se tiene @@ -2787,7 +2787,7 @@ donde . Si existe el límite de estas sumas cuando -\begin_inset Formula $|P|:=\sup\{t_{i}-t_{i-1}\}_{i=1}^{n}$ +\begin_inset Formula $|P|\coloneqq \sup\{t_{i}-t_{i-1}\}_{i=1}^{n}$ \end_inset tiende a 0 se dice que @@ -2840,7 +2840,7 @@ Vemos que si es la identidad entonces la integral es exactamente la de Riemann. Denotamos -\begin_inset Formula $\lambda_{\varphi}([a,b]):=\varphi(b)-\varphi(a)$ +\begin_inset Formula $\lambda_{\varphi}([a,b])\coloneqq \varphi(b)-\varphi(a)$ \end_inset . @@ -3045,11 +3045,11 @@ Demostración: . Sean -\begin_inset Formula $P:=\{a=x_{0}<\dots<x_{n}=b\}$ +\begin_inset Formula $P\coloneqq \{a=x_{0}<\dots<x_{n}=b\}$ \end_inset y -\begin_inset Formula $Q:=\{a=y_{0}<\dots<y_{m}=b\}$ +\begin_inset Formula $Q\coloneqq \{a=y_{0}<\dots<y_{m}=b\}$ \end_inset particiones con @@ -3245,15 +3245,15 @@ Demostración: \end_inset , -\begin_inset Formula $x_{1}:=t_{0}=a\in[\xi_{0},\xi_{1}]$ +\begin_inset Formula $x_{1}\coloneqq t_{0}=a\in[\xi_{0},\xi_{1}]$ \end_inset , -\begin_inset Formula $x_{i}:=t_{i-1}\in[\xi_{i-1},\xi_{i}]\forall i\in\{1,\dots,n\}$ +\begin_inset Formula $x_{i}\coloneqq t_{i-1}\in[\xi_{i-1},\xi_{i}]\forall i\in\{1,\dots,n\}$ \end_inset y -\begin_inset Formula $x_{n+1}:=t_{n}=b\in[\xi_{n},\xi_{n+1}]$ +\begin_inset Formula $x_{n+1}\coloneqq t_{n}=b\in[\xi_{n},\xi_{n+1}]$ \end_inset . |