diff options
Diffstat (limited to 'fvv2')
| -rw-r--r-- | fvv2/n1.lyx | 10 | ||||
| -rw-r--r-- | fvv2/n2.lyx | 6 | ||||
| -rw-r--r-- | fvv2/n3.lyx | 16 | ||||
| -rw-r--r-- | fvv2/n4.lyx | 2 |
4 files changed, 17 insertions, 17 deletions
diff --git a/fvv2/n1.lyx b/fvv2/n1.lyx index 7f67d1f..e7eda47 100644 --- a/fvv2/n1.lyx +++ b/fvv2/n1.lyx @@ -208,7 +208,7 @@ gráfica a \begin_inset Formula \[ -\text{graf}(f):=\{(x_{1},\dots,x_{n},y)\in\mathbb{R}^{n+1}:(x_{1},\dots,x_{n})\in[a_{1},b_{1}]\times\dots\times[a_{n},b_{n}]\land y=f(x_{1},\dots,x_{n})\} +\text{graf}(f):=\{(x_{1},\dots,x_{n},y)\in\mathbb{R}^{n+1}\mid (x_{1},\dots,x_{n})\in[a_{1},b_{1}]\times\dots\times[a_{n},b_{n}]\land y=f(x_{1},\dots,x_{n})\} \] \end_inset @@ -221,7 +221,7 @@ subgrafo \begin_inset Formula \begin{multline*} \text{subgraf}(f):=\\ -\{(x_{1},\dots,x_{n},y)\in\mathbb{R}^{n+1}:(x_{1},\dots,x_{n})\in[a_{1},b_{1}]\times\dots\times[a_{n},b_{n}]\land0\leq y\leq f(x_{1},\dots,x_{n})\} +\{(x_{1},\dots,x_{n},y)\in\mathbb{R}^{n+1}\mid (x_{1},\dots,x_{n})\in[a_{1},b_{1}]\times\dots\times[a_{n},b_{n}]\land0\leq y\leq f(x_{1},\dots,x_{n})\} \end{multline*} \end_inset @@ -1452,7 +1452,7 @@ Sea \end_inset , -\begin_inset Formula $B:=\{x\in A:\text{osc}(f,x)\geq\varepsilon\}$ +\begin_inset Formula $B:=\{x\in A\mid \text{osc}(f,x)\geq\varepsilon\}$ \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 $B:=\{x\in R:f\text{ no es continua en }x\}$ +\begin_inset Formula $B:=\{x\in R\mid f\text{ no es continua en }x\}$ \end_inset tiene medida nula. @@ -1559,7 +1559,7 @@ status open \end_inset Sea -\begin_inset Formula $B_{k}:=\{x\in R:o(f,x)\geq\frac{1}{k}\}$ +\begin_inset Formula $B_{k}:=\{x\in R\mid o(f,x)\geq\frac{1}{k}\}$ \end_inset , basta probar que cada diff --git a/fvv2/n2.lyx b/fvv2/n2.lyx index 56b1b12..bd555e8 100644 --- a/fvv2/n2.lyx +++ b/fvv2/n2.lyx @@ -654,7 +654,7 @@ espacio de medida \end_inset -finita si y sólo si -\begin_inset Formula $\{x\in\Omega:f(x)>0\}$ +\begin_inset Formula $\{x\in\Omega\mid f(x)>0\}$ \end_inset es numerable. @@ -889,7 +889,7 @@ medida exterior como \begin_inset Formula \[ -\lambda_{n}^{*}(B):=\inf\left\{ \sum_{k\in\mathbb{N}}v([a_{k},b_{k})):B\subseteq\dot{\bigcup_{k\in\mathbb{N}}}[a_{k},b_{k})\right\} +\lambda_{n}^{*}(B):=\inf\left\{ \sum_{k\in\mathbb{N}}v([a_{k},b_{k}))\mid B\subseteq\dot{\bigcup_{k\in\mathbb{N}}}[a_{k},b_{k})\right\} \] \end_inset @@ -1146,7 +1146,7 @@ Para \end_inset , y por tanto -\begin_inset Formula $\lambda_{n}^{*}(S)=\inf\{\lambda_{n}^{*}(A):A\supseteq S\text{ abierto}\}$ +\begin_inset Formula $\lambda_{n}^{*}(S)=\inf\{\lambda_{n}^{*}(A)\mid A\supseteq S\text{ abierto}\}$ \end_inset . diff --git a/fvv2/n3.lyx b/fvv2/n3.lyx index a35f67f..11ac40c 100644 --- a/fvv2/n3.lyx +++ b/fvv2/n3.lyx @@ -172,7 +172,7 @@ status open \end_inset Sea -\begin_inset Formula ${\cal A}:=\{E\in\Sigma':f^{-1}(E)\in\Sigma\}$ +\begin_inset Formula ${\cal A}:=\{E\in\Sigma'\mid f^{-1}(E)\in\Sigma\}$ \end_inset , vemos que @@ -627,7 +627,7 @@ Una función \end_inset y la notación -\begin_inset Formula $\{f\bullet a\}:=\{\omega\in\Omega:f(\omega)\bullet a\}$ +\begin_inset Formula $\{f\bullet a\}\mid =\{\omega\in\Omega\mid f(\omega)\bullet a\}$ \end_inset . @@ -1554,7 +1554,7 @@ Sea \end_inset y -\begin_inset Formula ${\cal S}(\Omega)^{+}:=\{h\in{\cal S}(\Omega):h\geq0\}$ +\begin_inset Formula ${\cal S}(\Omega)^{+}:=\{h\in{\cal S}(\Omega)\mid h\geq0\}$ \end_inset , llamamos @@ -1719,7 +1719,7 @@ Para medible, se define \begin_inset Formula \[ -\int f\,d\mu:=\sup\left\{ \int s\,d\mu:s\in{\cal S}(\Omega)\land0\leq s\leq f\right\} +\int f\,d\mu:=\sup\left\{ \int s\,d\mu\mid s\in{\cal S}(\Omega)\land0\leq s\leq f\right\} \] \end_inset @@ -2236,7 +2236,7 @@ Una función medible \end_inset , si y sólo si -\begin_inset Formula $f^{+}=\max\{f,0\},f^{-}=\min\{f,0\}:\Omega\rightarrow[-\infty,+\infty]$ +\begin_inset Formula $f^{+}=\max\{f,0\},f^{-}=\min\{f,0\}\mid \Omega\rightarrow[-\infty,+\infty]$ \end_inset son integrables, y definimos @@ -3315,11 +3315,11 @@ Demostración: \end_inset es continua, y como -\begin_inset Formula $\delta:=\min\{d(x,K):x\notin A\}>0$ +\begin_inset Formula $\delta:=\min\{d(x,K)\mid x\notin A\}>0$ \end_inset , -\begin_inset Formula $A_{0}:=\{x:d(x,K)<\frac{\delta}{2}\}$ +\begin_inset Formula $A_{0}:=\{x\mid d(x,K)<\frac{\delta}{2}\}$ \end_inset es un abierto acotado con @@ -3328,7 +3328,7 @@ Demostración: . Tomando -\begin_inset Formula $F_{0}:=\mathbb{R}^{n}\backslash A_{0}=\{x:d(x,K)\geq\frac{\delta}{2}\}$ +\begin_inset Formula $F_{0}:=\mathbb{R}^{n}\backslash A_{0}=\{x\mid d(x,K)\geq\frac{\delta}{2}\}$ \end_inset , podemos definir diff --git a/fvv2/n4.lyx b/fvv2/n4.lyx index 6628b45..2db00c5 100644 --- a/fvv2/n4.lyx +++ b/fvv2/n4.lyx @@ -360,7 +360,7 @@ teorema \end_inset es acotada y -\begin_inset Formula $D(f):=\{x\in[a,b]:f\text{ es discontinua en }x\}$ +\begin_inset Formula $D(f):=\{x\in[a,b]\mid f\text{ es discontinua en }x\}$ \end_inset , entonces |