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A question from Selected Topics in Integral Geometry
I'm referring to Gel'fand, Gindikin, and Graev's Selected Topics in Integral Geometry, pages 4-5, section 1.4 (see here and here).
Now in page 5 they write that:
$$dx_1 dx_2 = d(\xi_1 x_1 +\xi_2 x_2 ...
