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defs [2022/03/16 07:40] 127.0.0.1 external edit |
defs [2025/01/29 09:34] (current) rdouc |
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| Line 8: | Line 8: | ||
| \newcommand{\b}[1]{{\mathbf{#1}}} | \newcommand{\b}[1]{{\mathbf{#1}}} | ||
| \newcommand{\ball}[1]{\mathsf{B}(#1)} | \newcommand{\ball}[1]{\mathsf{B}(#1)} | ||
| + | \newcommand{\bbQ}{{\mathbb Q}} | ||
| \newcommand{\bproof}{\textbf{Proof :}\quad} | \newcommand{\bproof}{\textbf{Proof :}\quad} | ||
| \newcommand{\bmuf}[2]{b_{#1,#2}} | \newcommand{\bmuf}[2]{b_{#1,#2}} | ||
| \newcommand{\card}{\mathrm{card}} | \newcommand{\card}{\mathrm{card}} | ||
| \newcommand{\chunk}[3]{{#1}_{#2:#3}} | \newcommand{\chunk}[3]{{#1}_{#2:#3}} | ||
| + | \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} | ||
| \newcommand{\convprob}[1]{\stackrel{#1-\text{prob}}{\rightarrow}} | \newcommand{\convprob}[1]{\stackrel{#1-\text{prob}}{\rightarrow}} | ||
| \newcommand{\Cov}{\mathbb{C}\mathrm{ov}} | \newcommand{\Cov}{\mathbb{C}\mathrm{ov}} | ||
| + | \newcommand{\cro}[1]{\langle #1 \rangle} | ||
| \newcommand{\CPE}[2]{\PE\lr{#1| #2}} | \newcommand{\CPE}[2]{\PE\lr{#1| #2}} | ||
| - | |||
| \renewcommand{\det}{\mathrm{det}} | \renewcommand{\det}{\mathrm{det}} | ||
| \newcommand{\dimlabel}{\mathsf{m}} | \newcommand{\dimlabel}{\mathsf{m}} | ||
| Line 34: | Line 36: | ||
| \renewcommand{\geq}{\geqslant} | \renewcommand{\geq}{\geqslant} | ||
| \newcommand{\hchi}{\hat \chi} | \newcommand{\hchi}{\hat \chi} | ||
| + | \newcommand{\Hset}{\mathsf{H}} | ||
| \newcommand{\Id}{\mathrm{Id}} | \newcommand{\Id}{\mathrm{Id}} | ||
| \newcommand{\img}{\text{Im}} | \newcommand{\img}{\text{Im}} | ||
| Line 40: | Line 43: | ||
| \newcommand{\indin}[1]{\mathbf{1}\{#1\}} | \newcommand{\indin}[1]{\mathbf{1}\{#1\}} | ||
| \newcommand{\itemm}{\quad \quad \blacktriangleright \;} | \newcommand{\itemm}{\quad \quad \blacktriangleright \;} | ||
| + | \newcommand{\jointtrans}[3]{p_{#1}(#2,#3)} | ||
| \newcommand{\ker}{\text{Ker}} | \newcommand{\ker}{\text{Ker}} | ||
| \newcommand{\klbck}[2]{\mathrm{K}\lr{#1||#2}} | \newcommand{\klbck}[2]{\mathrm{K}\lr{#1||#2}} | ||
| Line 47: | Line 51: | ||
| \renewcommand{\leq}{\leqslant} | \renewcommand{\leq}{\leqslant} | ||
| \newcommand{\lone}{\mathsf{L}_1} | \newcommand{\lone}{\mathsf{L}_1} | ||
| + | \newcommand{\lp}[1]{\mathsf{L}_{{#1}}} | ||
| \newcommand{\lrav}[1]{\left|#1 \right|} | \newcommand{\lrav}[1]{\left|#1 \right|} | ||
| \newcommand{\lr}[1]{\left(#1 \right)} | \newcommand{\lr}[1]{\left(#1 \right)} | ||
| Line 62: | Line 67: | ||
| \right\vert\kern-0.25ex\right\vert\kern-0.25ex\right\vert}} | \right\vert\kern-0.25ex\right\vert\kern-0.25ex\right\vert}} | ||
| \newcommand{\nset}{\mathbb N} | \newcommand{\nset}{\mathbb N} | ||
| + | \newcommand{\N}{\mathcal{N}} | ||
| \newcommand{\one}{\mathsf{1}} | \newcommand{\one}{\mathsf{1}} | ||
| \newcommand{\PE}{\mathbb E} | \newcommand{\PE}{\mathbb E} | ||
| + | \newcommand{\pminfty}{_{-\infty}^\infty} | ||
| \newcommand{\PP}{\mathbb P} | \newcommand{\PP}{\mathbb P} | ||
| + | \newcommand{\projorth}[1]{\mathsf{P}^\perp_{#1}} | ||
| \newcommand{\Psif}{\Psi_f} | \newcommand{\Psif}{\Psi_f} | ||
| \newcommand{\pscal}[2]{\langle #1,#2\rangle} | \newcommand{\pscal}[2]{\langle #1,#2\rangle} | ||
| Line 70: | Line 78: | ||
| \newcommand{\psconv}{\stackrel{\PP-a.s.}{\rightarrow}} | \newcommand{\psconv}{\stackrel{\PP-a.s.}{\rightarrow}} | ||
| \newcommand{\qset}{\mathbb Q} | \newcommand{\qset}{\mathbb Q} | ||
| + | \newcommand{\revcondtrans}[3]{q_{#1}(#2|#3)} | ||
| \newcommand{\rmd}{\mathrm d} | \newcommand{\rmd}{\mathrm d} | ||
| \newcommand{\rme}{\mathrm e} | \newcommand{\rme}{\mathrm e} | ||
| Line 88: | Line 97: | ||
| \newcommand{\tv}[1]{\left\|#1\right\|_{\mathrm{TV}}} | \newcommand{\tv}[1]{\left\|#1\right\|_{\mathrm{TV}}} | ||
| \newcommand{\unif}{\mathrm{Unif}} | \newcommand{\unif}{\mathrm{Unif}} | ||
| + | \newcommand{\weaklim}[1]{\stackrel{\mathcal{L}_{#1}}{\rightsquigarrow}} | ||
| \newcommand{\Xset}{{\mathsf X}} | \newcommand{\Xset}{{\mathsf X}} | ||
| \newcommand{\Xsigma}{\mathcal X} | \newcommand{\Xsigma}{\mathcal X} | ||
defs.1647412810.txt.gz ยท Last modified: 2022/03/16 07:40 by 127.0.0.1
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