From: Pierre-Cyrille Heam Date: Thu, 19 Jan 2012 15:05:25 +0000 (+0100) Subject: Merge branch 'master' of ssh://info.iut-bm.univ-fcomte.fr/prng_gpu X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/prng_gpu.git/commitdiff_plain/3010272fc200ffae4e9223ba48c5f3caf05a4256 Merge branch 'master' of ssh://info.iut-bm.univ-fcomte.fr/prng_gpu Conflicts: prng_gpu.tex --- 3010272fc200ffae4e9223ba48c5f3caf05a4256 diff --cc prng_gpu.tex index 0a88df5,20e2566..55fc756 --- a/prng_gpu.tex +++ b/prng_gpu.tex @@@ -789,7 -807,7 +810,11 @@@ where $(s^0,s^1, \hdots)$ is the strate claimed in the lemma. \end{proof} ++<<<<<<< HEAD +We can now prove the Theorem~\ref{t:chaos des general}. ++======= + We can now prove Theorem~\ref{t:chaos des general}... ++>>>>>>> e55d237aba022a66cc2d7650d295b29169878f45 \begin{proof}[Theorem~\ref{t:chaos des general}] Firstly, strong transitivity implies transitivity. @@@ -1206,8 -1232,8 +1239,10 @@@ $y\bigoplus_{i=1}^{i=j} w_i^\prime=y\bi by a direct induction, that $w_i=w_i^\prime$. Furthermore, since $\mathbb{B}^{kN}$ is finite, each $\varphi_y$ is bijective. Therefore, and using (\ref{PCH-1}), one has ++$\mathrm{Pr}[D^\prime(U_{kN})=1]=\mathrm{Pr}[D(\varphi_y(U_{kN}))=1]$ and, ++therefore, \begin{equation}\label{PCH-2} --\mathrm{Pr}[D^\prime(U_{kN})=1]=\mathrm{Pr}[D(\varphi_y(U_{kN}))=1]=\mathrm{Pr}[D(U_{kN})=1]. ++\mathrm{Pr}[D^\prime(U_{kN})=1]=\mathrm{Pr}[D(U_{kN})=1]. \end{equation} Now, using (\ref{PCH-1}) again, one has for every $x$,