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On the manifold of closed hypersurfaces in $\mathbb{R}^n$
Integration with vector valued measures
1. | Unversity of California, Riverside, Riverside, CA 92521, Uruguay |
References:
[1] |
S. Bochner, "Harmonic Analysis and the Theory of Probability," University of California Press, Berkely, CA, 1956. |
[2] |
N. Dunford and J. T. Schwartz , "Linear Operators, Part I: General Theory," Wiley-Interscience, New York, 1958. |
[3] |
P. L. Duren, "Theory of $H^p$ Spaces," Academic Press, New York, 1970. |
[4] |
W. Feller, "An Introduction to Probability Theory and its Applications, Vol. 2," Wiley, New York, 1966. . |
[5] |
D. J. H. Garling, Non-negative random measures and order preserving embeddings, J. London Math. Soc. (2), 11, (1975), 35-45. .
doi: 10.1112/jlms/s2-11.1.35. |
[6] |
S. Kakutani, Über die Metrisation der topologischen Grouppen, Proc. Imp. Acad. Tokyo, 12,(1936), 82-84.
doi: 10.3792/pia/1195580206. |
[7] |
N. J. Kalton, N. T. Peck and J. W. Roberts, $L^0$-valued vector measures are bounded, Proc. Amer. Math. Soc., 85, (1982), 575-582.
doi: 10.2307/2044069. |
[8] |
V. L. Klee, Invariant metrics in groups:(Solution of a problem of Banach), Proc. Amer. Math. Soc., 3, (1952), 484-487.
doi: 10.1090/S0002-9939-1952-0047250-4. |
[9] |
T. V. Panchapagesan, "The Bartle-Dunford-Schwartz Integral," Birkhäuser Verlag AG, Basel, (2008). |
[10] |
A. Prékopa, On stochastic set functions, I-III, Acta Math. Acad. Sci. Hungary, 8, (1956), 215-263; (1957),337-374; 375-400.
doi: 10.1007/BF02020323. |
[11] |
M. M. Rao, Random measures and applications, Stochastic Anal. Appl., 27, (2009), 1014-1076.
doi: 10.1080/07362990903136546. |
[12] |
M. M. Rao, "Random and Vector Measures," World Scientific, Singapore, 2012. |
[13] |
M. M. Rao, "Measure Theory and Integration," Wiley-Interscience, and Marcel Dekker, New York, 1987, 2nd ed., 2004. |
[14] |
M. M. Rao and Z. D. Ren , "Theory of Orlicz Spaces," Marcel Dekker, New York, 1991. |
[15] |
M. M. Rao and Z. D. Ren , "Applications of Orlicz Spaces," Marcel Dekker, New York, 2002.
doi: 10.1201/9780203910863. |
[16] | |
[17] |
I. Shragin, "Superpositional Measurability and Superposition Operator, (Selected Themes)," Odessa, "Astroprint'', 2007. |
[18] |
M. S. Steigerwalt and A. J. White , Some function spaces related to $L_p$, Proc. London Math. Soc., 22, (1971), 137-163.
doi: 10.1112/plms/s3-22.1.137. |
[19] |
M. Talagrand, Les mesures vectorielles a valuers dans $L^0$ sont bournées, Ann. Sci. Ècole Norm. asup., 14,(1981), 445-452. |
[20] |
K. Urbanik, Some prediction problems for strictly stationary processes, Proc. 5th Berkely Symp. Math. Statist. and Prob., 2, part 1, (1967), 235-258. |
[21] |
V. M. Zolotarev, "One Dimensional Stable Distributions," Translatios A.M.S., 65, Providence, R.I., 1986. |
show all references
References:
[1] |
S. Bochner, "Harmonic Analysis and the Theory of Probability," University of California Press, Berkely, CA, 1956. |
[2] |
N. Dunford and J. T. Schwartz , "Linear Operators, Part I: General Theory," Wiley-Interscience, New York, 1958. |
[3] |
P. L. Duren, "Theory of $H^p$ Spaces," Academic Press, New York, 1970. |
[4] |
W. Feller, "An Introduction to Probability Theory and its Applications, Vol. 2," Wiley, New York, 1966. . |
[5] |
D. J. H. Garling, Non-negative random measures and order preserving embeddings, J. London Math. Soc. (2), 11, (1975), 35-45. .
doi: 10.1112/jlms/s2-11.1.35. |
[6] |
S. Kakutani, Über die Metrisation der topologischen Grouppen, Proc. Imp. Acad. Tokyo, 12,(1936), 82-84.
doi: 10.3792/pia/1195580206. |
[7] |
N. J. Kalton, N. T. Peck and J. W. Roberts, $L^0$-valued vector measures are bounded, Proc. Amer. Math. Soc., 85, (1982), 575-582.
doi: 10.2307/2044069. |
[8] |
V. L. Klee, Invariant metrics in groups:(Solution of a problem of Banach), Proc. Amer. Math. Soc., 3, (1952), 484-487.
doi: 10.1090/S0002-9939-1952-0047250-4. |
[9] |
T. V. Panchapagesan, "The Bartle-Dunford-Schwartz Integral," Birkhäuser Verlag AG, Basel, (2008). |
[10] |
A. Prékopa, On stochastic set functions, I-III, Acta Math. Acad. Sci. Hungary, 8, (1956), 215-263; (1957),337-374; 375-400.
doi: 10.1007/BF02020323. |
[11] |
M. M. Rao, Random measures and applications, Stochastic Anal. Appl., 27, (2009), 1014-1076.
doi: 10.1080/07362990903136546. |
[12] |
M. M. Rao, "Random and Vector Measures," World Scientific, Singapore, 2012. |
[13] |
M. M. Rao, "Measure Theory and Integration," Wiley-Interscience, and Marcel Dekker, New York, 1987, 2nd ed., 2004. |
[14] |
M. M. Rao and Z. D. Ren , "Theory of Orlicz Spaces," Marcel Dekker, New York, 1991. |
[15] |
M. M. Rao and Z. D. Ren , "Applications of Orlicz Spaces," Marcel Dekker, New York, 2002.
doi: 10.1201/9780203910863. |
[16] | |
[17] |
I. Shragin, "Superpositional Measurability and Superposition Operator, (Selected Themes)," Odessa, "Astroprint'', 2007. |
[18] |
M. S. Steigerwalt and A. J. White , Some function spaces related to $L_p$, Proc. London Math. Soc., 22, (1971), 137-163.
doi: 10.1112/plms/s3-22.1.137. |
[19] |
M. Talagrand, Les mesures vectorielles a valuers dans $L^0$ sont bournées, Ann. Sci. Ècole Norm. asup., 14,(1981), 445-452. |
[20] |
K. Urbanik, Some prediction problems for strictly stationary processes, Proc. 5th Berkely Symp. Math. Statist. and Prob., 2, part 1, (1967), 235-258. |
[21] |
V. M. Zolotarev, "One Dimensional Stable Distributions," Translatios A.M.S., 65, Providence, R.I., 1986. |
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