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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
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An alternative to complete topological vector spaces in the framework of condensed mathematics.
Roughly, completeness is expressed as ability to integrate with respect to Radon measures.
This doesnâ€™t quite work as stated, and to make this rigorous one has to bring L^p-spaces for $0\lt p\le 1$ (i.e., the non-convex case) into the picture.
A condensed abelian group $V$ is $p$-liquid ($0\lt p\le 1$) if for every compact Hausdorff topological space $S$ and every morphism of condensed sets $f\colon S\to V$ there is a unique morphism of condensed abelian groups $M_{<p}(S)\to V$ that extends $f$ along the inclusion $S\to M_{<p}(S)$.
Here for a compact Hausdorff topological space $S$ and for any $p$ such that $0<p\le 1$ we have
$M_{<p}(S)=\bigcup_{q<p}M_q(S),$where
$M_p(S)=\bigcup_{C>0}M(S)_{\ell^p\le C},$where
$M(S)_{\ell^p\le C}=\lim_i M(S_i)_{\ell^p\le C},$where $S_i$ are finite sets such that
$S = \lim_i S_i$and
$M(F)_{\ell^p\le C}$for a finite set $F$ denotes the subset of $\mathbf{R}^F$ consisting of sequence with l^p-norm at most $C$.
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