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authorJuan Marin Noguera <juan@mnpi.eu>2022-12-04 22:49:17 +0100
committerJuan Marin Noguera <juan@mnpi.eu>2022-12-04 22:49:17 +0100
commitc34b47089a133e58032fe4ea52f61efacaf5f548 (patch)
tree4242772e26a9e7b6f7e02b1d1e00dfbe68981345 /fvv2/n4.lyx
parent214b20d1614b09cd5c18e111df0f0d392af2e721 (diff)
Oops
Diffstat (limited to 'fvv2/n4.lyx')
-rw-r--r--fvv2/n4.lyx28
1 files changed, 14 insertions, 14 deletions
diff --git a/fvv2/n4.lyx b/fvv2/n4.lyx
index 2db00c5..ada1c91 100644
--- a/fvv2/n4.lyx
+++ b/fvv2/n4.lyx
@@ -103,11 +103,11 @@ Dados dos espacios medibles
rectángulo medible
\series default
en
-\begin_inset Formula $\Omega:=\Omega_{1}\times\Omega_{2}$
+\begin_inset Formula $\Omega\coloneqq \Omega_{1}\times\Omega_{2}$
\end_inset
a los elementos de
-\begin_inset Formula ${\cal R}:=\{A\times B\}_{A\in\Sigma_{1},B\in\Sigma_{2}}$
+\begin_inset Formula ${\cal R}\coloneqq \{A\times B\}_{A\in\Sigma_{1},B\in\Sigma_{2}}$
\end_inset
.
@@ -124,7 +124,7 @@ rectángulo medible
\end_inset
a
-\begin_inset Formula $\Sigma:=\Sigma_{1}\times\Sigma_{2}:=\sigma({\cal R})$
+\begin_inset Formula $\Sigma\coloneqq \Sigma_{1}\times\Sigma_{2}\coloneqq \sigma({\cal R})$
\end_inset
.
@@ -224,11 +224,11 @@ medida imagen
\end_inset
a la medida
-\begin_inset Formula $\nu:=\mu g^{-1}:\Sigma'\rightarrow[0,+\infty]$
+\begin_inset Formula $\nu\coloneqq \mu g^{-1}:\Sigma'\rightarrow[0,+\infty]$
\end_inset
dada por
-\begin_inset Formula $\nu(A):=\mu(g^{-1}(A))$
+\begin_inset Formula $\nu(A)\coloneqq \mu(g^{-1}(A))$
\end_inset
.
@@ -360,7 +360,7 @@ teorema
\end_inset
es acotada y
-\begin_inset Formula $D(f):=\{x\in[a,b]\mid f\text{ es discontinua en }x\}$
+\begin_inset Formula $D(f)\coloneqq \{x\in[a,b]\mid f\text{ es discontinua en }x\}$
\end_inset
, entonces
@@ -450,11 +450,11 @@ función de distribución
\end_inset
a
-\begin_inset Formula $F(x):=\mu(\{f\leq x\})$
+\begin_inset Formula $F(x)\coloneqq \mu(\{f\leq x\})$
\end_inset
o a
-\begin_inset Formula $\varphi(x):=\mu(\{f>x\})=\mu(\Omega)-F(x)$
+\begin_inset Formula $\varphi(x)\coloneqq \mu(\{f>x\})=\mu(\Omega)-F(x)$
\end_inset
.
@@ -463,11 +463,11 @@ función de distribución
\end_inset
una variable aleatoria,
-\begin_inset Formula $F(x):=\mu(\{f\leq x\})$
+\begin_inset Formula $F(x)\coloneqq \mu(\{f\leq x\})$
\end_inset
y
-\begin_inset Formula $\varphi(x):=\mu(\{f>x\})$
+\begin_inset Formula $\varphi(x)\coloneqq \mu(\{f>x\})$
\end_inset
, entonces
@@ -524,7 +524,7 @@ Si
\end_inset
no es acotada, podemos aplicar este resultado a los conjuntos
-\begin_inset Formula $E_{a,b}:=\{a<f\leq b\}$
+\begin_inset Formula $E_{a,b}\coloneqq \{a<f\leq b\}$
\end_inset
para
@@ -532,7 +532,7 @@ Si
\end_inset
cualesquiera definiendo
-\begin_inset Formula $\mu_{a,b}(E):=\mu(E\cap E_{a,b})$
+\begin_inset Formula $\mu_{a,b}(E)\coloneqq \mu(E\cap E_{a,b})$
\end_inset
y usando esta medida.
@@ -601,7 +601,7 @@ Si
\end_inset
es medible con
-\begin_inset Formula $\varphi(x):=\mu(\{f>x\})$
+\begin_inset Formula $\varphi(x)\coloneqq \mu(\{f>x\})$
\end_inset
y
@@ -673,7 +673,7 @@ Llamamos
\end_inset
, escribimos
-\begin_inset Formula ${\cal L}^{p}(\mu):={\cal L}_{\phi}(\mu)$
+\begin_inset Formula ${\cal L}^{p}(\mu)\coloneqq {\cal L}_{\phi}(\mu)$
\end_inset
.