Absolutely continuous and locally quasi-invariant measures on locally compact semigroups

Dzinotyiweyi, Henry A. M.

doi:10.1090/S0002-9939-1978-0476907-4

Absolutely continuous and locally quasi-invariant measures on locally compact semigroups
HTML articles powered by AMS MathViewer

by Henry A. M. Dzinotyiweyi PDF

Proc. Amer. Math. Soc. 69 (1978), 49-55 Request permission

Abstract:

Let S be a locally compact semigroup and T a locally compact subsemigroup of S. It is shown that, for a large class of semigroups S, if T is ’reasonably large’, the absolutely continuous measures on T extend to measures whose translates by some points of S are absolutely continuous on S. As a consequence we prove the absolute continuity of translates of some measures related to a locally quasi-invariant measure.

References

Anne C. Baker and J. W. Baker, Algebras of measures on a locally compact semigroup, J. London Math. Soc. (2) 1 (1969), 249–259. MR 245713, DOI 10.1112/jlms/s2-1.1.249
Anne C. Baker and J. W. Baker, Algebras of measures on a locally compact semigroup. II, J. London Math. Soc. (2) 2 (1970), 651–659. MR 274639, DOI 10.1112/jlms/2.Part_{4}.651
Anne C. Baker and J. W. Baker, Algebras of measures on a locally compact semigroup. III, J. London Math. Soc. (2) 4 (1972), 685–695. MR 306806, DOI 10.1112/jlms/s2-4.4.685
Henry A. M. Dzinotyiweyi, Locally quasi-invariant measures, J. London Math. Soc. (2) 15 (1977), no. 3, 484–488. MR 442201, DOI 10.1112/jlms/s2-15.3.484
A. Grothendieck, Sur les applications linéaires faiblement compactes d’espaces du type $C(K)$, Canad. J. Math. 5 (1953), 129–173 (French). MR 58866, DOI 10.4153/cjm-1953-017-4

Abstract harmonic analysis

28

Neal J. Rothman, An $L^{1}$ algebra for certain locally compact topological semigroups, Pacific J. Math. 23 (1967), 143–151. MR 215112
N. J. Rothman and M. W. Schuh, Laplace tranforms on vanishing algebras, Semigroup Forum 8 (1974), no. 3, 189–214. MR 384983, DOI 10.1007/BF02194763

Convolution measure algebras on semigroups

James D. Stein Jr., Uniform absolute continuity in spaces of set functions, Proc. Amer. Math. Soc. 51 (1975), 137–140. MR 440012, DOI 10.1090/S0002-9939-1975-0440012-0
Stephen Willard, General topology, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1970. MR 0264581
James C. S. Wong, Absolutely continuous measures on locally compact semigroups, Canad. Math. Bull. 18 (1975), no. 1, 127–132. MR 380268, DOI 10.4153/CMB-1975-023-3