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Lineage of the Theory of Invariant Integrals on Groups

Takeshi Hirai

Abstract: From the standpoint of the History of Mathematics, beginning with pioneering work of Hurwitz on invariant integrals (or invariant measures) on Lie groups, we pick up epoch-making works successively and draw the main stream among so many contributions to the study of invariant integrals on groups, due to Hurwitz, Schur, Weyl, Haar, Neumann, Kakutani, Weil, and Kakutani-Kodaira, and explain their contents and give the relationships among them.
Keywords: invariant integrals / making works / works successively / epoch making / Kakutani Kodaira / pioneering work / invariant measures / Lie groups

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