MathOverflow

Let $\mu$ and $\nu$ be two probability measures on $\mathbb{R}^{d}$.
Let $T : \mathbb{R}^{d} \rightarrow \mathbb{R}^{d}$ be a measurable map such that $T_{\ast} \mu = \nu$.I can disintegrate $\gamma := (id,T)_{\ast} \mu$ according to $(h, h_{\ast} \gamma$): I get a family of measures $\gamma_{y}$ concentred on $h^{-1...

I'm reading Knutson's book on algebraic spaces, and I stumbled over the quasi-separatedness axiom in his definition of algebraic spaces (Definition 1.1, Chapter II). He defines an algebraic space $A$ as a sheaf on the site of schemes with the étale topology...

(Update, July 15, 2026): Using a higher search radius, Simon Goater found,
while Jeff Braun found (June 27, 2026),
Guruprasad's earlier search radius of $|x|<20000$ found $6$ (and more) like,

Is it possible to constructively prove that every $q \in \mathbb H$ has some $r$ such that $r^2 = q$? The difficulty here is that $q$ might be a negative scalar, in which case there might be "too many" values of $r$. Namely, $r$ could then equal any...