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$\mathrm{\{}\mathit{a}\mathrm{,}$ $\mathit{b}\mathrm{)}\mathrm{\subset }\mathit{u}\mathrm{(}\mathit{G}\mathrm{\left)}\mathrm{\Omega }\mathrm{\right(}\mathit{a}\mathrm{,}\mathrm{}\mathit{b}\mathrm{)}\mathrm{\cap }{\mathit{G}}_{\mathrm{2}}$. $\mathrm{(}\mathit{a}\mathrm{,}\mathrm{}\mathit{b}\mathrm{)}\mathrm{\subset }\mathit{u}\mathrm{\left(}\mathit{G}\mathrm{\right)}\mathrm{,}$ $\mathit{b}\mathrm{\to }\mathrm{\infty }\mathrm{,}$ ${\mathit{\mu }}_{{\mathit{G}}_{\mathrm{1}}}\mathrm{(}\mathit{a}\mathrm{,}\mathrm{}\mathit{b}\mathrm{)}\mathrm{(}\tilde{\mathit{\rho }}\mathrm{,}\mathrm{}\mathit{\rho }\mathrm{)}\mathrm{=}\mathrm{\left|}\mathrm{\right|}\mathit{\rho }\mathrm{\left|}{\mathrm{|}}^{\mathrm{2}}\mathrm{\right|}\mathrm{\left|}\mathit{\rho }\mathrm{\right|}\mathrm{|}\mathrm{\le }\mathrm{|}\mathrm{\left|}{\mathit{\rho }}_{\mathit{G}}\mathrm{\right|}\mathrm{|}$. ${\mathrm{\Gamma }}_{{\mathit{G}}_{\mathrm{1}}\mathrm{\cup }\mathrm{\text{...}}\mathrm{\cup }{\mathit{G}}_{\mathit{k}}}\mathrm{(}\mathit{a}\mathrm{,}\mathrm{}\mathit{b}\mathrm{)}$,

$\mathrm{(}{\mathit{\rho }}_{\mathit{G}}\mathrm{,}\mathrm{}\mathit{\rho }\mathrm{)}\mathrm{\prime }\mathrm{=}\mathrm{\left|}\mathrm{\right|}\mathit{\rho }\mathrm{|}{\mathrm{|}}^{\mathrm{2}}\mathrm{,}$ $\mathrm{(}{\mathit{\rho }}_{\mathit{G}}\mathrm{,}$ $\mathrm{\&}\mathrm{)}$ $\mathrm{=}{{\displaystyle \int }}_{\mathit{a}}^{\mathit{b}}{\mathrm{\Theta }}^{\mathrm{-}\mathrm{1}}\mathit{d}\mathit{c}{\mathrm{\Theta }}_{\mathit{G}}\mathrm{\left(}\mathit{c}\mathrm{\right)}\mathrm{=}{{\displaystyle \int }}_{\mathit{l}\mathrm{\left(}\mathit{c}\mathrm{\right)}\mathrm{\cap }\mathit{G}}\mathrm{|}\mathrm{-}\mathrm{*}\mathit{d}\mathit{u}\mathrm{|}$.

$\mathit{u}\mathit{u}{\mathit{G}}_{\mathrm{1}}{\mathit{G}}_{\mathrm{1}}{\mathit{G}}_{\mathrm{2}}{\mathit{\rho }}_{\mathit{G}}\tilde{\mathit{\rho }}{\mathit{G}}_{\mathrm{2}}\mathrm{,}$ $\mathrm{\Theta }\mathrm{\ge }{\mathrm{\Theta }}_{\mathit{G}}\mathrm{,}$ $\mathrm{\Gamma }\mathrm{(}\mathit{a}\mathrm{,}\mathrm{}\mathit{b}\mathrm{)}\mathrm{,}$ ${\mathit{\mu }}_{\mathit{G}}\mathrm{(}\mathit{a}\mathrm{,}\mathrm{}\mathit{b}\mathrm{)}\mathrm{\Omega }\mathrm{(}\mathit{a}\mathrm{,}\mathrm{}\mathit{b}\mathrm{)}\mathrm{,}$ $\mathrm{\left|}\mathrm{\right|}\mathit{\rho }\mathrm{\left|}\mathrm{\right|}\mathrm{<}\mathrm{\infty }\mathrm{\left|}\mathrm{\right|}\mathit{\rho }\mathrm{\left|}\mathrm{\right|}\mathrm{<}\mathrm{\infty }{\mathit{G}}_{\mathrm{1}}$, ..., ${\mathit{G}}_{\mathit{k}}\mathrm{,}$ ${\mathrm{\Gamma }}_{\mathit{G}}\mathrm{(}\mathit{a}\mathrm{,}\mathrm{}\mathit{b}\mathrm{)}$.

${\mathit{\mu }}_{\mathit{G}\mathrm{*}}\mathrm{(}\mathit{a}\mathrm{,}\mathrm{}\mathit{b}\mathrm{)}\mathrm{\Omega }\mathrm{(}\mathit{a}\mathrm{,}\mathrm{}\mathit{b}\mathrm{)}\mathrm{\cap }\mathit{G}\mathrm{-}\mathrm{\infty }\mathrm{\le }\mathit{a}\mathrm{<}\mathit{b}\mathrm{\le }\mathrm{\infty }$. $\mathrm{\Omega }\mathrm{(}\mathit{a}\mathrm{,}\mathrm{}\mathit{b}\mathrm{)}$ tl ${\mathit{G}}_{\mathrm{1}}$

$\mathrm{(}\mathrm{\prime }\mathit{a}\mathrm{,}\mathrm{}\mathit{b}\mathrm{)}\mathrm{\subset }\mathit{u}\mathrm{\left(}{\mathit{G}}_{\mathit{j}}\mathrm{\right)}\mathrm{,}$ $\mathit{j}\mathrm{=}\mathrm{1}\mathrm{,}$ $\mathrm{\text{...}}\mathrm{,}$ $\mathit{k}\mathrm{,}$ ${\mathit{\mu }}_{\mathit{G}}\mathrm{(}\mathit{a}\mathrm{,}\mathrm{}\mathit{b}\mathrm{)}\mathrm{=}{{\displaystyle \int }}_{\mathit{a}}^{\mathit{b}}\frac{\mathit{d}\mathit{c}}{{\mathrm{\Theta }}_{\mathit{G}}\mathrm{\left(}\mathit{c}\mathrm{\right)}}\mathrm{,}{\tilde{\mathit{\rho }}}_{{\mathit{G}}_{\mathrm{1}}}$. ... . ${\mathit{G}}_{\mathit{k}}\mathrm{=}\frac{\mathrm{1}}{\mathit{k}}{\displaystyle \sum }_{\mathit{J}\mathrm{=}\mathrm{1}}^{\mathit{k}}{\mathit{\rho }}_{{\mathit{G}}_{\mathit{j}}}\mathrm{,}$ $\mathrm{\left|}\mathrm{\right|}{\mathit{\rho }}_{\mathit{G}}\mathrm{-}\mathit{\rho }\mathrm{|}{\mathrm{|}}^{\mathrm{2}}\mathrm{=}\mathrm{|}\mathrm{\left|}{\mathit{\rho }}_{\mathit{G}}\mathrm{\right|}{\mathrm{|}}^{\mathrm{2}}\mathrm{-}\mathrm{\left|}\mathrm{\right|}\mathit{\rho }\mathrm{|}{\mathrm{|}}^{\mathrm{2}}$.

$\mathrm{|}\tilde{\mathit{\rho }}\mathrm{-}\mathit{\rho }\mathrm{|}{\mathrm{|}}^{\mathrm{2}}\mathrm{=}\mathrm{\left|}\mathrm{\right|}\tilde{\mathit{\rho }}\mathrm{|}{\mathrm{|}}^{\mathrm{2}}\mathrm{-}\mathrm{|}\mathrm{\left|}\mathit{\rho }\mathrm{\right|}{\mathrm{|}}^{\mathrm{2}}$. $\mathrm{\left|}\mathrm{\right|}\mathit{\rho }\mathrm{\left|}\mathrm{\right|}\mathrm{\le }\mathrm{\left|}\mathrm{\right|}{\mathit{\rho }}_{{\mathit{G}}_{\mathrm{1}\mathrm{\cup }\mathrm{\text{...}}\mathrm{\cup }}{\mathit{G}}_{\mathit{k}}}\mathrm{\left|}\mathrm{\right|}\mathrm{\le }\mathrm{\left|}\mathrm{\right|}\tilde{\mathit{\rho }}\mathrm{\left|}\mathrm{\right|}$. $\mathrm{\left|}\mathrm{\right|}\tilde{\mathit{\rho }}\mathrm{|}{\mathrm{|}}^{\mathrm{2}}\mathrm{=}\frac{\mathrm{1}}{{\mathit{k}}^{\mathrm{2}}}{\displaystyle \sum }_{\mathit{j}\mathrm{=}\mathrm{1}}^{\mathit{k}}\mathrm{|}\mathrm{\left|}{\mathit{\rho }}_{{\mathit{G}}_{\mathit{j}}}\mathrm{\right|}{\mathrm{|}}^{\mathrm{2}}$.

${\mathrm{\Theta }}^{\mathrm{-}\mathrm{1}}\mathrm{\le }$ $\mathrm{(}{\mathrm{\Theta }}_{{\mathit{G}}_{\mathrm{1}\mathrm{\cup }}}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{}\mathrm{\cup }{\mathit{G}}_{\mathit{k}}{\mathrm{)}}^{\mathrm{-}\mathrm{1}}\mathrm{=}\mathrm{(}{\displaystyle \sum }{\mathrm{\Theta }}_{{\mathit{G}}_{\mathit{f}}}{\mathrm{)}}^{\mathrm{-}\mathrm{1}}\mathrm{\le }{\mathit{k}}^{\mathrm{-}\mathrm{2}}{\displaystyle \sum }\mathrm{(}{\mathrm{\Theta }}_{{\mathit{G}}_{\mathit{l}}}{\mathrm{)}}^{\mathrm{-}\mathrm{1}}$. ${{\displaystyle \int }}_{\mathit{a}}^{\mathit{b}}\frac{\mathit{d}\mathit{c}}{\mathrm{\Theta }\mathrm{\left(}\mathit{c}\mathrm{\right)}}\mathrm{\le }{{\displaystyle \int }}_{\mathit{a}}^{\mathit{b}}\frac{\mathit{d}\mathit{c}}{{\mathrm{\Theta }}_{{\mathit{G}}_{\mathrm{1}}\mathrm{\cup }\mathrm{\text{...}}\mathrm{\cup }{\mathit{G}}_{\mathit{k}}}\mathrm{\left(}\mathit{c}\mathrm{\right)}}\mathrm{\le }\frac{\mathrm{1}}{{\mathit{k}}^{\mathrm{2}}}{\displaystyle \sum }_{\mathit{J}\mathrm{\iff }\mathrm{1}}^{\mathit{k}}{{\displaystyle \int }}_{\mathit{a}}^{\mathit{b}}\frac{\mathit{d}\mathit{c}}{{\mathrm{\Theta }}_{{\mathit{G}}_{\mathit{j}}}\mathrm{\left(}\mathit{c}\mathrm{\right)}}$

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