diff options
Diffstat (limited to 'fvv2/n2.lyx')
| -rw-r--r-- | fvv2/n2.lyx | 36 |
1 files changed, 18 insertions, 18 deletions
diff --git a/fvv2/n2.lyx b/fvv2/n2.lyx index bd555e8..0442b74 100644 --- a/fvv2/n2.lyx +++ b/fvv2/n2.lyx @@ -123,7 +123,7 @@ Un \end_inset y -\begin_inset Formula $A\Delta B:=(A\backslash B)\cup(B\backslash A)\in{\cal A}$ +\begin_inset Formula $A\Delta B\coloneqq (A\backslash B)\cup(B\backslash A)\in{\cal A}$ \end_inset (diferencia simétrica). @@ -177,11 +177,11 @@ Una \end_inset , tomando la sucesión creciente -\begin_inset Formula $U_{n}:=\bigcup_{k=1}^{n}A_{k}$ +\begin_inset Formula $U_{n}\coloneqq \bigcup_{k=1}^{n}A_{k}$ \end_inset , vemos que -\begin_inset Formula $A:=\bigcup_{n\in\mathbb{N}}A_{n}=\bigcup_{n\in\mathbb{N}}U_{n}\in{\cal A}$ +\begin_inset Formula $A\coloneqq \bigcup_{n\in\mathbb{N}}A_{n}=\bigcup_{n\in\mathbb{N}}U_{n}\in{\cal A}$ \end_inset . @@ -239,7 +239,7 @@ Si \end_inset es un conjunto de álgebras, su intersección -\begin_inset Formula $\Sigma:=\bigcap_{\alpha\in A}\Sigma_{\alpha}$ +\begin_inset Formula $\Sigma\coloneqq \bigcap_{\alpha\in A}\Sigma_{\alpha}$ \end_inset es un álgebra, y si los @@ -314,7 +314,7 @@ Sea \end_inset a -\begin_inset Formula ${\cal B}(T):=\sigma({\cal J})=\sigma({\cal F})$ +\begin_inset Formula ${\cal B}(T)\coloneqq \sigma({\cal J})=\sigma({\cal F})$ \end_inset , y sus elementos son los @@ -356,7 +356,7 @@ Dados \end_inset , escribimos -\begin_inset Formula $[a,b):=\prod_{i=1}^{n}[a_{i},b_{i})$ +\begin_inset Formula $[a,b)\coloneqq \prod_{i=1}^{n}[a_{i},b_{i})$ \end_inset , y definimos @@ -634,7 +634,7 @@ espacio de medida \end_inset , -\begin_inset Formula $\Sigma:={\cal P}(\Omega)$ +\begin_inset Formula $\Sigma\coloneqq {\cal P}(\Omega)$ \end_inset y @@ -642,7 +642,7 @@ espacio de medida \end_inset , la función dada por -\begin_inset Formula $\mu(E):=\sum_{x\in E}f(x)$ +\begin_inset Formula $\mu(E)\coloneqq \sum_{x\in E}f(x)$ \end_inset es una medida en @@ -718,11 +718,11 @@ Subaditividad \end_inset Si llamamos -\begin_inset Formula $B_{1}:=A_{1}$ +\begin_inset Formula $B_{1}\coloneqq A_{1}$ \end_inset y -\begin_inset Formula $B_{n}:=A_{n}\backslash\bigcup_{k=1}^{n-1}A_{k}$ +\begin_inset Formula $B_{n}\coloneqq A_{n}\backslash\bigcup_{k=1}^{n-1}A_{k}$ \end_inset para @@ -1181,7 +1181,7 @@ Demostración: . Entonces -\begin_inset Formula $\lambda_{n}^{*}(A:=\bigcup_{k=1}^{+\infty}(a'_{k},b_{k}))\leq\sum_{k=1}^{+\infty}((a'_{k},b_{k}))<\sum_{k=1}^{+\infty}(v([a_{k},b_{k}))+\frac{\varepsilon}{2^{k+1}})=\sum_{k=1}^{+\infty}[a_{k},b_{k})+\frac{\varepsilon}{2}<\lambda_{n}^{*}(S)+\frac{\varepsilon}{2}+\frac{\varepsilon}{2}=\lambda_{n}^{*}(S)+\varepsilon$ +\begin_inset Formula $\lambda_{n}^{*}(A\coloneqq \bigcup_{k=1}^{+\infty}(a'_{k},b_{k}))\leq\sum_{k=1}^{+\infty}((a'_{k},b_{k}))<\sum_{k=1}^{+\infty}(v([a_{k},b_{k}))+\frac{\varepsilon}{2^{k+1}})=\sum_{k=1}^{+\infty}[a_{k},b_{k})+\frac{\varepsilon}{2}<\lambda_{n}^{*}(S)+\frac{\varepsilon}{2}+\frac{\varepsilon}{2}=\lambda_{n}^{*}(S)+\varepsilon$ \end_inset . @@ -1217,7 +1217,7 @@ Lebesgue medida de Lebesgue \series default es -\begin_inset Formula $\lambda_{n}(M):=\lambda_{n}^{*}(M)$ +\begin_inset Formula $\lambda_{n}(M)\coloneqq \lambda_{n}^{*}(M)$ \end_inset . @@ -1242,7 +1242,7 @@ teorema \end_inset tal que su intersección -\begin_inset Formula $B:=\bigcap_{k}A_{k}$ +\begin_inset Formula $B\coloneqq \bigcap_{k}A_{k}$ \end_inset cumple que @@ -1293,7 +1293,7 @@ conjuntos y un conjunto de medida nula. Si -\begin_inset Formula $M:=\bigcup_{k}M_{k}$ +\begin_inset Formula $M\coloneqq \bigcup_{k}M_{k}$ \end_inset es unión numerable de conjuntos medibles, @@ -1429,7 +1429,7 @@ Demostración: \end_inset -\begin_inset Formula $B:=\bigcap_{k}A_{k}$ +\begin_inset Formula $B\coloneqq \bigcap_{k}A_{k}$ \end_inset tl que @@ -1751,7 +1751,7 @@ Si la medida exterior de \end_inset tiene medida nula y como -\begin_inset Formula $H:=\bigcup_{k}H_{k}$ +\begin_inset Formula $H\coloneqq \bigcup_{k}H_{k}$ \end_inset es medible, entonces @@ -1844,7 +1844,7 @@ Si \end_inset , donde -\begin_inset Formula $c:=\mu([0,1)^{n})$ +\begin_inset Formula $c\coloneqq \mu([0,1)^{n})$ \end_inset . @@ -1970,7 +1970,7 @@ teorema para transformaciones lineales \end_inset , donde -\begin_inset Formula $c:=\lambda_{n}(T([0,1)^{n}))=|\det(T)|$ +\begin_inset Formula $c\coloneqq \lambda_{n}(T([0,1)^{n}))=|\det(T)|$ \end_inset . |