Geodesic
Admissible transformations of measures
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 1 (2005), pp. 155-181.

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Let a topological semigroup $G$ acts on a topological space $X$. A transformation $g\in G$ is called an admissible (partially admissible, singular, equivalent, invariant) transform for $\mu$ relative to $\nu$ if $\mu_g\ll\nu$ (accordingly: $\mu_g\not\perp\nu$, $\mu_g\perp\nu$, $\mu_g\sim\nu$, $\mu_g=c\cdot\nu$), where $\mu_g(E):=\mu(g^{-1}E)$. We denote its collection by $A(\mu|\nu)$ (accordingly: $AP(\mu|\nu)$, $S(\mu|\nu)$, $E(\mu|\nu)$, $I(\mu|\nu)$). The algebraic and the measure theoretical properties of these sets are studied. It is done the Lebesgue-type decomposition. If $G=X$ is a locally compact group, we give some informations about the measure theoretical size of $A(\mu)$. 
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S. S. Gabrielyan. Admissible transformations of measures. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 1 (2005), pp. 155-181. http://geodesic.mathdoc.fr/item/JMAG_2005_1_a1/

[1] S. S. Gabriyelyan, “On absolutely continuity and singularity of probability measures”, Ukr. Mat. Zh., 2005 (to appear) (Russian)

[2] A. V. Skorohod, “On admissible translations of measures in Hilbert space”, Theory Probab. Appl., 15:4 (1970), 577–598 | MR

[3] A. V. Skorohod, Integration in Hilbert space, Nauka, Moscow, 1975 (Russian) | MR

[4] E. Hewitt, K. Ross, Abstract harmonic analysis, v. 1, Academic Press, New York, 1963

[5] P. L. Brockett, “Admissible transformations of measures”, Semigroup Forum, 12 (1976), 21–33 | DOI | MR | Zbl

[6] S. Kakutani, “On equivalence of infinite product measures”, Ann. Math., 49 (1948), 214–224 | DOI | MR | Zbl

[7] G. W. Mackey, “Borel structure in groups and their duals”, Trans. Amer. Math. Soc., 85 (1957), 134–165 | DOI | MR | Zbl

[8] Y. Okazaki, “Admissible translates of measures on a topological group”, Mem. Fac. Sci. Kyushu Univ., A34 (1980), 79–88 | DOI | MR | Zbl

[9] T. S. Pitcher, “The admissible mean values of stochastic process”, Trans. Amer. Math. Soc., 108 (1980), 538–546 | DOI | MR