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Results tagged with counterexamples
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user 99469
A counterexample is an example that disproves a mathematical conjecture or a purported theorem. For example, the Peterson graph is a counterexample to many seemingly plausible conjectures in Graph Theory.
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Is a $\sigma$-algebra generated by complete independent $\sigma$-algebras also complete?
$
\newcommand{\cA}{\mathcal{A}}
\newcommand{\cB}{\mathcal{B}}
\newcommand{\sP}{\mathscr{P}}
$
Let $(\Omega, \cA, \mu)$ be a probability space and $\cA_1, \cA_2$ sub $\sigma$-algebras of $\cA$. Let $\c …
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Is there $\varepsilon \in (0, 1)$ such that $\sup_{t \in [0, \varepsilon]} [\ell_t]_\beta < ...
$
\newcommand{\bR}{\mathbb{R}}
\newcommand{\bT}{\mathbb{T}}
\newcommand{\bN}{\mathbb{N}}
\newcommand{\bP}{\mathbb{P}}
\newcommand{\bE}{\mathbb{E}}
\newcommand{\bF}{\mathbb{F}}
\newcommand{\bD}{\mathbb …
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