Abstract
A proof of the formula\(\int\limits_U {f \circ \varphi |\det D_\varphi |d\mu } = \int\limits_{\varphi (U)} {f d\mu } \) for locally compact fields\(\mathbb{K}\) andC 1-isomorphisms ϕ:U→V, whereU andV are open subsets of\(\mathbb{K}^n \), was never published. In this paper we give two short proofs, one of them is a more elementary variant of the other.
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References
Abhyankar, S. S.: Local Analytic Geometry. New York-London: Academic Press. 1964.
Bourbaki, N.: Algebra I. Reading, MA: Addison-Wesley. 1974.
Bourbaki, N.: Variétés Différentielles et Analytiques, Fascicule de résultats. Paris: Diffusion, C.C.L.S. 1983.
Braconnier, J.: Sur les groupes topologiques localement compacts. J. Math. Pures Appl. (9)27, 1–85 (1948).
Dieudonné, J.: Treatise on Analysis III. New York-London: Academic Press. 1972.
Hörmander, L.: An Introduction to Complex Analysis in Several Variables. Princeton N. J.: van Nostrand. 1966.
Kneser, M.: Semi-simple algebraic groups. In: Algebraic Number Theory. (ed. byJ. W. S. Cassels andA. Fröhlich). New York: Academic Press. 1967.
Schwartz, J.: The Formula for Change in Variables in a Multiple Integral. Am. Math. Monthly61, 81–85 (1954).
Weil, A.: Basic Number Theory. 3rd ed. Berlin-Heidelberg-New York: Springer. 1974.
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Schoissengeier, J. Change of variables in a multiple integral for local fields. Monatshefte für Mathematik 114, 139–147 (1992). https://doi.org/10.1007/BF01535581
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DOI: https://doi.org/10.1007/BF01535581