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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.

1 vote
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116 views

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 …
1 vote
1 answer
104 views

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 …