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For the proof of Theorem 16 see page 225 of "Introduction to Measure and Integration" by S.J. Taylor or page 98 of "Real Analysis" by H.L. Royden.
References: H.L. Royden, "Real Analysis" ; W. Rudin, "Real and Complex Analysis" ; Wheeden and Zygmund "Real Analysis". 5. MATH520 (Differentiable Manifolds and Lie Groups)
Royden, Real Analysis ... Topics include general properties of Lie groups and Lie algebras, Peter-Weyl ...
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