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Register a new userPseudoquotient extensions of measure spaces
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Authors
Piotr Mikusinski
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A space of pseudoquotients $mathcal P (X,S)$ is defined as equivalence classes of pairs $(x,f)$, where $x$ is an element of a non-empty set $X$, $f$ is an element of $S$, a commutative semigroup of injective maps from $X$ to $X$, and $(x,f) sim (y,g)$ if $gx=fy$. In this note we assume that $(X,Sigma,mu)$ is a measure space and that $S$ is a commutative semigroup of measurable injections acting on $X$ and investigate under what conditions there is an extension of $mu$ to $mathcal P (X,S)$.
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