Klasična teorija invariantnih mer, ki ima pomembno vlogo v teoriji parakoksalnih dekompozicij, temelji na pojmu "psevdogrupa". Take prevdogrupe so konkretni zgledi Boolovih inverznih monoidov, ki so ...povezane z etalnimi topološkimi groupoidi preko nekomutativne Stonove dualnosti. V članku proučujemo teorijo invariantnih mer na poljubnih Boolovih inverznih monoidih. V našem glavnem rezultatu karakteriziramo, kdaj lahko ima Boolov inverzni monoid invariantno mero. Ta rezultat posploši klasično alternativo Tarskega, ki sta jo z uporabo drugih metod dokazala npr. de la Harpe in Skandalis.
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