Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1999 | 159 | 1 | 71-84
Tytuł artykułu

On products of Radon measures

Treść / Zawartość
Warianty tytułu
Języki publikacji
Let $X = [0,1]^Γ$ with card Γ ≥ c (c denotes the continuum). We construct two Radon measures μ,ν on X such that there exist open subsets of X × X which are not measurable for the simple outer product measure. Moreover, these measures are strikingly similar to the Lebesgue product measure: for every finite F ⊆ Γ, the projections of μ and ν onto $[0,1]^F$ are equivalent to the F-dimensional Lebesgue measure. We generalize this construction to any compact group of weight ≥ c, by replacing the Lebesgue product measure with the Haar measure.
Słowa kluczowe
Opis fizyczny
  • Department of Mathematics, University of Athens, Panepistimiopolis 15784, Athens, Greece
  • Department of Mathematics, University of Athens, Panepistimiopolis 15784, Athens, Greece
  • [B-F] B. Balcar and F. Franek, Independent families in complete Boolean algebras, Trans. Amer. Math. Soc. 274 (1982), 607-618.
  • [Bo] N. Bourbaki, Intégration, Ch. 8, Hermann, Paris, 1959-1967.
  • [C] J. R. Choksi, Recent developments arising out of Kakutani's work on completion regularity of measures, in: Contemp. Math. 26, Amer. Math. Soc., Providence, R.I., 1984, 81-94.
  • [E] B. A. Efimov, Mappings and embeddings of dyadic spaces, Mat. Sb. 103 (1977), 52-68 (in Russian).
  • [Er-Ox] P. Erdős and J. C. Oxtoby, Partitions of the plane into sets having positive measure in every non-null measurable product set, Trans. Amer. Math. Soc. 79 (1955), 91-102.
  • [Fr₁] D. H. Fremlin, Products of Radon measures: a counter-example, Canad. Math. Bull. 19 (1976), 285-289.
  • [Fr₂] D. H. Fremlin, Measure Theory, University of Essex, Colchester, 1994.
  • [Fr-Gr] D. H. Fremlin and S. Grekas, Products of completion regular measures, Fund. Math. 147 (1995), 27-37.
  • [Gr₁] S. Grekas, Structural properties of compact groups with measure-theoretic applications, Israel J. Math. 87 (1994), 89-95.
  • [Gr₂] S. Grekas, Measure-theoretic problems in topological dynamics, J. Anal. Math. 65 (1995), 207-220.
  • [Gr-Me] S. Grekas and S. Mercourakis, On the measure theoretic structure of compact groups, Trans. Amer. Math. Soc. 350 (1998), 2779-2796.
  • [Gry] C. Gryllakis, Products of completion regular measures, Proc. Amer. Math. Soc. 103 (1988), 563-568.
  • [H] R. Haydon, On Banach spaces which contain $l^1(τ)$ and types of measures on compact spaces, Israel J. Math. 28 (1977), 313-324.
  • [He-Ro] E. Hewitt and K. Ross, Abstract Harmonic Analysis I, Springer, Berlin, 1963.
  • [K] V. Kuz'minov, On a hypothesis of P. S. Aleksandrov in the theory of topological groups, Dokl. Akad. Nauk SSSR 125 (1959), 727-729 (in Russian).
  • [Mo-Zi] D. Montgomery and L. Zippin, Topological Transformation Groups, Interscience, 1955.
  • [Mos] P. S. Mostert, Sections in principal fibre spaces, Duke Math. J. 23 (1956), 57-71.
  • [P] A. Pełczyński, Linear extensions, linear averagings, and their applications to linear topological classification of spaces of continuous functions, Dissertationes Math. 58 (1968).
  • [Pr] J. F. Price, Lie Groups and Compact Groups, Cambridge Univ. Press, 1977.
  • [T₁] M. Talagrand, Pettis integral and measure theory, Mem. Amer. Math. Soc. 307 (1984).
  • DUPA[T₂] M. Talagrand, On liftings and the regularization of stochastic processes, Probab. Theory Related Fields 78 (1988), 127-134.
  • [U] V. V. Uspenskiĭ, Why compact groups are dyadic, in: General Topology and its Relations to Modern Analysis and Algebra VI, Proc. Sixth Prague Topological Symposium 1986, Z. Frolík (ed.), Heldermann, Berlin, 1988, 601-610.
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.