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An approach to the theory of integration and theory of Lebesgue-Bochner measurable functions on locally compact spaces

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References

  1. Bogdanowicz, W. M.: A generalization of the Lebesgue-Bochner-Stieltjes integral and a new approach to the theory of integration. Proc. Nat. Acad. Sci. USA53, 492–498 (1965).

    Google Scholar 

  2. —— Integral representations of linear continuous operators from the space of Lebesgue-Bochner summable functions into any Banach space. Proc. Nat. Acad. Sci. USA54, 351–354 (1965).

    Google Scholar 

  3. —— An approach to the theory ofL p spaces of Lebesgue-Bochner summable functions and generalized Lebesgue-Bochner-Stieltjes integral. Bull. Acad. Polon. Sci.13, 793–800 (1965).

    Google Scholar 

  4. —— Integral representations of linear continuous operators onL p spaces of Lebesgue-Bochner summable functions. Bull. Acad. Polon. Sci.13, 801–808 (1965).

    Google Scholar 

  5. —— An approach to the theory of Lebesgue-Bochner measurable function and the theory of measure. Math. Ann.164, 251–269 (1966).

    Google Scholar 

  6. -- An approach to the theory of integration generated by positive functionals and integral representations of linear continuous functionals on the space of vector valued continuous functions. To appear in Math. Ann.

  7. -- Fubini theorems for generalized Lebesgue-Bochner-Stieltjes integral. To appear in Trans. Amer. Math. Soc., for announcement of the results see Proc. Japan Acad.42 (1966), [supplement to41, 979–983 (1965)].

  8. Bochner, S.: Integration von Funktionen, deren Werte die Elemente eines Vektorraumes sind. Fundamenta Math.20, 262–276 (1933).

    Google Scholar 

  9. Bourbaki, N.: Eléments de mathématique, Integration. Actualités Sci. Ind. No. 1175 (1952), No. 1244 (1956), No. 1281 (1959).

  10. Dunford, N., andJ. Schwartz: Linear Operators Vol.1. New York: Interscience 1958.

    Google Scholar 

  11. Gelfand, I.: Abstrakte Funktionen und lineare Operatoren. Mat. Sborn.4, 235–284 (1938).

    Google Scholar 

  12. Halmos, P.-R.: Measure Theory. New York: D. van Nostrand Co., Inc., 1950.

    Google Scholar 

  13. Köthe, G.: Topologische lineare Räume I. Berlin-Göttingen-Heidelberg: Springer 1960.

    Google Scholar 

  14. Pettis, B. J.: On integration in vector spaces. Trans. Am. Math. Soc.44, 277–304 (1939).

    Google Scholar 

  15. Bogdanowicz, W. M.: On volumes generating the same Lebesgue-Bochner integration. Proc. Nat. Acad. Sci. USA56, 1399–1405 (1966).

    Google Scholar 

  16. -- Relations between complete integral seminorms, measures and volumes. To appear in Dissertationes Mathematicae (previous name: Rozprawy Matematyczne).

  17. -- Remarks on Lebesgue-Bochner integration. Vectorial integration generated by complete integral seminorms. To appear in Dissertationes Mathematicae (previous name: Rozprawy Matematyczne).

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  1. Department of Mathematics, Catholic Univ. of America, 20017, Washington, DC, USA

    Witold M. Bogdanowicz

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  1. Witold M. Bogdanowicz
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Bogdanowicz, W.M. An approach to the theory of integration and theory of Lebesgue-Bochner measurable functions on locally compact spaces. Math. Ann. 171, 219–238 (1967). https://doi.org/10.1007/BF01362040

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