[Merged by Bors] - chore(analysis/mean_inequalities): split mean_inequalities into two files #10355
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…iles (#10355) This PR puts all results related to power functions into a new file. Currently, we prove convexity of `exp` and `pow`, then use those properties in `mean_inequalities`. I am refactoring some parts of the analysis library to reduce the use of derivatives. I want to prove convexity of exp without derivatives (in a future PR), prove Holder's inequality, then use it to prove the convexity of pow. This requires Holder's inequality to be in a file that does not use convexity of pow, hence the split. I needed to change the proof of Holder's inequality since it used the generalized mean inequality (hence `pow`). I switched to the second possible proof mentioned in the file docstring. I also moved some lemmas in `mean_inequalities` to have three main sections: AM-GM, then Young and a final section with Holder and Minkowski.
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This PR puts all results related to power functions into a new file.
Currently, we prove convexity of
expandpow, then use those properties inmean_inequalities. I am refactoring some parts of the analysis library to reduce the use of derivatives. I want to prove convexity of exp without derivatives (in a future PR), prove Holder's inequality, then use it to prove the convexity of pow. This requires Holder's inequality to be in a file that does not use convexity of pow, hence the split.I needed to change the proof of Holder's inequality since it used the generalized mean inequality (hence
pow). I switched to the second possible proof mentioned in the file docstring.I also moved some lemmas in
mean_inequalitiesto have three main sections: AM-GM, then Young and a final section with Holder and Minkowski.The result of the whole refactor can be seen in the (stale) branch
pow_split.