23/05/17 23:47:25.68 X9rwP1Sp.net
youtube 解説動画が落ちていた
14：36秒もの
証明を読むたしには、なりそう
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Looman Menchoff Theorem
Young Measures
59 回視聴 2023/03/16
If you have partial derivatives then they do not even imply continuity of a function let alone its differentiability (example in video).
But if those partials satisfy the Cauchy-Riemann equations, the function is holomorphic. In particular it is C-infinity smooth and even analytic.