Density measures and additive property

Preprint English OPEN
Kunisada, Ryoichi (2015)
  • Subject: 11B05, 46E27 | Mathematics - Number Theory

We deal with finitely additive measures defined on all subsets of natural numbers which extend the asymptotic density (density measures). We consider a class of density measures which are constructed from free ultrafilters on natural numbers and study a certain additivity property of such density measures.
  • References (15)
    15 references, page 1 of 2

    [1] A. Basile, K. P. S. Bhaskara Rao, Completeness of Lp-Spaces in the Finitely Additive Setting and Related Stories, J. Math. Anal. Appl. 248, (2000) 588-624.

    [2] W. C. Bell, J. W. Hagood, Completeness of Lp spaces and Radon-Nikodym theorems for unbounded finitely additive measures, J. Math. Anal. Appl. 218 (1998) 82-96.

    [3] K. P. S. Bhaskara Rao, M. Bhaskara Rao, Theory of charges, Academic Press, London, 1983.

    [4] A. Blass, R. Frankiewicz, G. Plebanek, C. Ryll-Nardzewski, A note on extensions of asymptotic density, Proc. Amer. Math. Soc. 129 (11) (2001) 3313-3320.

    [5] M. Blu¨mlinger, Levy group action and invariant measures on βN, Trans. Amer. Math. Soc. 348 (12) (1996) 5087-5111.

    [6] R. C. Buck, The measure theoretic approach to density, Amer. J. Math. 68 (1946) 560-580.

    [7] C. Chou, Minimal sets and ergodic measures for βN \ N, Illinois J. Math. 13 (1969) 777-788.

    [8] P. Letavaj, L. Miˇs´ık, M. Sleziak, Extreme points of the set of density measures, J. Math. Anal. Appl. 423 (2015) 1150-1165.

    [9] D. Maharam, Finitely additive measures on the integers, Sankhya Ser. A 38 (1976) 44-59.

    [10] A. H. Mekler, Finitely additive measures on N and the additive property, Porc. Amer. Math. Soc. 92 (1984) 439-444.

  • Metrics
    3
    views in OpenAIRE
    0
    views in local repository
    0
    downloads in local repository
Share - Bookmark