Öz
Kaynakça
- [1] N.K. Agbeko, On optimal averages, Acta Math. Hungar. 63(2)(1994), 133–147.
- [2] N.K. Agbeko, On the structure of optimal measures and some of its applications, Publ. Math. Debrecen 46(1-2)(1995), 79–87.
- [3] V.I. Bogachev, Measure Theory, vol 1, Springer-Verlag Berlin Heidelberg 2007.
- [4] C. Caratheodory, Vorlesungen über reelle Funktionen, Amer. Math. Soc. 2004.
- [5] L. Drewnowski, A representation theorem for maxitive measures, Indag. Math. (N.S.), 20(1)(2009), 43–47.
- [6] L.C. Evans, R.F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, Inc., 1992. ISBN: 0-8493-7157-0
- [7] D. Harte, Multifractals. Theory and Applications, Chapman and Hall / Crc, Boca Raton London New York Washington D.C, 2001. ISBN 1-58488-154-2
- [8] A.N. Kolmogorov, and S.V. Fomin, Elements of the Theory of Functions and Functional Analysis, Graylack Press, Albany, N. Y. 1961.
- [9] H. Lebesgue, Sur une generalistion de l’integrale definie, C.R. Acad.Sci. Paris 132(1901), 1025-1028.
- [10] H. Lebesgue, Integrale, longueur, aire, Ann. Mat. Pura Appl. 7(1902), 231-359.
- [11] J.C. Robinson, Dimensions, Embeddings, and Attractors, Cambridge University Press, Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Dubai, Tokyo, Mexico City, 2011.
- [12] N. Shilkret, Maxitive measure and integration, Indag. Math., 33(1971), 109-116.
- [13] E.M. Taylor, Measure theory and integration, Graduate Studies in Mathematics, 76, 2006. ISBN: 13 978-0-8218-4180-8.
Öz
Substituting in the definition of outer measure the addition with the maximum (or the supremum, or the join) operation we obtain a new set function called retuo measure. It is proved that every retuo measure is an outer measure. We give necessary and sufficient conditions for a set function to be a retuo measure. Similarly as in the case of outer measure, we propose a way to construct retuo measures. We consider some theoretical applications for constructed pairs of outer and retuo measures in the image of the Hausdorff measure and dimension.
Anahtar Kelimeler
outer mearsure sigma-algebra measurable sets Hausdorff measure Hausdorff dimension Caratheodory-type theorem
Kaynakça
- [1] N.K. Agbeko, On optimal averages, Acta Math. Hungar. 63(2)(1994), 133–147.
- [2] N.K. Agbeko, On the structure of optimal measures and some of its applications, Publ. Math. Debrecen 46(1-2)(1995), 79–87.
- [3] V.I. Bogachev, Measure Theory, vol 1, Springer-Verlag Berlin Heidelberg 2007.
- [4] C. Caratheodory, Vorlesungen über reelle Funktionen, Amer. Math. Soc. 2004.
- [5] L. Drewnowski, A representation theorem for maxitive measures, Indag. Math. (N.S.), 20(1)(2009), 43–47.
- [6] L.C. Evans, R.F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, Inc., 1992. ISBN: 0-8493-7157-0
- [7] D. Harte, Multifractals. Theory and Applications, Chapman and Hall / Crc, Boca Raton London New York Washington D.C, 2001. ISBN 1-58488-154-2
- [8] A.N. Kolmogorov, and S.V. Fomin, Elements of the Theory of Functions and Functional Analysis, Graylack Press, Albany, N. Y. 1961.
- [9] H. Lebesgue, Sur une generalistion de l’integrale definie, C.R. Acad.Sci. Paris 132(1901), 1025-1028.
- [10] H. Lebesgue, Integrale, longueur, aire, Ann. Mat. Pura Appl. 7(1902), 231-359.
- [11] J.C. Robinson, Dimensions, Embeddings, and Attractors, Cambridge University Press, Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Dubai, Tokyo, Mexico City, 2011.
- [12] N. Shilkret, Maxitive measure and integration, Indag. Math., 33(1971), 109-116.
- [13] E.M. Taylor, Measure theory and integration, Graduate Studies in Mathematics, 76, 2006. ISBN: 13 978-0-8218-4180-8.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Articles |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Eylül 2020 |
| Yayımlandığı Sayı | Yıl 2020 Cilt: 3 Sayı: 3 |