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Informationsmaße Eq: math.2392.61

Hash: 161943c282e0fa2fc1085c22d80f2153

TeX (original user input):

\begin{align}

& {{P}_{i}}=\rho \left( {{x}^{i}} \right){{\Delta }^{d}}x \\

& I(P)=\sum\limits_{i}^{{}}{{}}{{\Delta }^{d}}x\rho \left( {{x}^{i}} \right)\ln \left( {{\Delta }^{d}}x\rho \left( {{x}^{i}} \right) \right)=\sum\limits_{i}^{{}}{{}}{{\Delta }^{d}}x\rho \left( {{x}^{i}} \right)\ln \left( \rho \left( {{x}^{i}} \right) \right)+\sum\limits_{i}^{{}}{{}}{{\Delta }^{d}}x\rho \left( {{x}^{i}} \right)\ln \left( {{\Delta }^{d}}x \right) \\

& \sum\limits_{i}^{{}}{{}}{{\Delta }^{d}}x\rho \left( {{x}^{i}} \right)=1 \\

& \sum\limits_{i}^{{}}{{}}{{\Delta }^{d}}x\rho \left( {{x}^{i}} \right)\ln \left( {{\Delta }^{d}}x \right)=const. \\

\end{align}

TeX (checked):

{\begin{aligned}&{{P}_{i}}=\rho \left({{x}^{i}}\right){{\Delta }^{d}}x\\&I(P)=\sum \limits _{i}^{}{}{{\Delta }^{d}}x\rho \left({{x}^{i}}\right)\ln \left({{\Delta }^{d}}x\rho \left({{x}^{i}}\right)\right)=\sum \limits _{i}^{}{}{{\Delta }^{d}}x\rho \left({{x}^{i}}\right)\ln \left(\rho \left({{x}^{i}}\right)\right)+\sum \limits _{i}^{}{}{{\Delta }^{d}}x\rho \left({{x}^{i}}\right)\ln \left({{\Delta }^{d}}x\right)\\&\sum \limits _{i}^{}{}{{\Delta }^{d}}x\rho \left({{x}^{i}}\right)=1\\&\sum \limits _{i}^{}{}{{\Delta }^{d}}x\rho \left({{x}^{i}}\right)\ln \left({{\Delta }^{d}}x\right)=const.\\\end{aligned}}

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\begin{aligned} P_{i} = ρ (x^{i}) Δ^{d} x \\ I (P) = \sum_{i}^{} Δ^{d} x ρ (x^{i}) \ln (Δ^{d} x ρ (x^{i})) = \sum_{i}^{} Δ^{d} x ρ (x^{i}) \ln (ρ (x^{i})) + \sum_{i}^{} Δ^{d} x ρ (x^{i}) \ln (Δ^{d} x) \\ \sum_{i}^{} Δ^{d} x ρ (x^{i}) = 1 \\ \sum_{i}^{} Δ^{d} x ρ (x^{i}) \ln (Δ^{d} x) = c o n s t . \end{aligned}

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Identifiers

$P_{i}$

$ρ$

$x$

$i$

$Δ$

$d$

$x$

$I$

$P$

$i$

$Δ$

$d$

$x$

$ρ$

$x$

$i$

$Δ$

$d$

$x$

$ρ$

$x$

$i$

$i$

$Δ$

$d$

$x$

$ρ$

$x$

$i$

$ρ$

$x$

$i$

$i$

$Δ$

$d$

$x$

$ρ$

$x$

$i$

$Δ$

$d$

$x$

$i$

$Δ$

$d$

$x$

$ρ$

$x$

$i$

$i$

$Δ$

$d$

$x$

$ρ$

$x$

$i$

$Δ$

$d$

$x$

$c$

$o$

$n$

$s$

$t$

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