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Past exam of the Probability, statistics and options II course of the University of Oxford / 2007 / D / 3 / ii / Solution by Codex 0 2026-10-31
The change of variables formula for a Lebesgue integrable function is
(1)
The absolute Jacobian determinant accounts for area regardless of orientation. The formula also holds for nonnegative measurable functions with possibly infinite integral.
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