Suatu Ukuran Bernilai C[a,b]
Keywords:
Ukuran luar Ukuran Himpunan terukur Ruang ukuran
Abstract
Dalam paper ini dikonstruksi suatu ukuran bernilai , dimana adalah koleksi semua fungsi kontinu bernilai real yang terdefinisi pada selang tertutup dan terbatas . Dalam mengkonstruksi ukuran bernilai tersebut, terlebih dahulu dikonstruksi ukuran luar bernilai . Kemudian membangkitkan ukuran melalui ukuran luar tersebut. Beberapa sifat sederhana yang berkaitan dengan ukuran bernilai juga akan dibahas dalam paper ini.
References
[1] Bartle, R.G., The Elements of Integration and Lebesgue Measure. John Wiley & Sons, New York; 1995.
[2] Boccuto, A., Riecan, B. and Vrabelova, M., Kurzweil-Henstock Integral in Riesz Spaces. Bentham Books; 2009.
[3] Ghoussoub, N., Riesz Spaces Valued Measures and Processes, Bull. Soc. Math. France, 1982. (110), hal. 233257
[4] Royden, H.L. and Fitzpatrick, P.M., Real Analysis, Fourth Edition, Pearson Education Asia Limited and China Machine Press; 2010.
[5] Ubaidillah, F., Darmawijaya, S., dan Rini, Ch. I., C[a,b]-Valued Measure and Some of Its Properties Proc. Int. Conf. on Research, Imp. and Edu. of Math. and Sci., Yogyakarta State University; 2014. hal. M21-M26
[6] Ubaidillah, F., Darmawijaya, S., dan Rini, Ch. I., On the Henstock-Kurzweil Integral of C[a; b] Space-valued Functions, Int. J. Math. An. 2015. 9 (37) hal. 1831 – 1846
[7] Wright, J.D.M., Measures with Values in a Partially Ordered Vector Space, Proc. London Math. Soc; 1972. 25 hal. 675- 688
[2] Boccuto, A., Riecan, B. and Vrabelova, M., Kurzweil-Henstock Integral in Riesz Spaces. Bentham Books; 2009.
[3] Ghoussoub, N., Riesz Spaces Valued Measures and Processes, Bull. Soc. Math. France, 1982. (110), hal. 233257
[4] Royden, H.L. and Fitzpatrick, P.M., Real Analysis, Fourth Edition, Pearson Education Asia Limited and China Machine Press; 2010.
[5] Ubaidillah, F., Darmawijaya, S., dan Rini, Ch. I., C[a,b]-Valued Measure and Some of Its Properties Proc. Int. Conf. on Research, Imp. and Edu. of Math. and Sci., Yogyakarta State University; 2014. hal. M21-M26
[6] Ubaidillah, F., Darmawijaya, S., dan Rini, Ch. I., On the Henstock-Kurzweil Integral of C[a; b] Space-valued Functions, Int. J. Math. An. 2015. 9 (37) hal. 1831 – 1846
[7] Wright, J.D.M., Measures with Values in a Partially Ordered Vector Space, Proc. London Math. Soc; 1972. 25 hal. 675- 688
Published
2017-07-31
Issue
Section
Mathematics
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