What do you think about this breakthrough in Fourier analysis

http://arxiv.org/abs/1602.05384 ]]>

I don’t quite understand some detail of the proof of Lusin’s theorem.

Why we control the measure of A by instead of ? What is the relation between and ? And how local uniform limits play any role?

I think that if we control , then we are almost done. Since , which is continuous, uniformly converges to outside of , then is continuous outside of , problem solved. What wrong with this?

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Ingenious. Thank you very much, you are a great inspiration. ]]>

Equivalently, it seems to me that

By some argument of monotone convergence?

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as one can see by considering what happens when .

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