What's the definition of "rate of uniform convergence"?

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What's the definition of "rate of uniform convergence"?

I'm reading "Understanding Machine Learning: From theory to algorithms". You can click the hyperlink to download the book.

I came across this phrase in the preface of Chapter 26: Rademacher Complexities, Page 375. I have looked up a lot of materials, but I didn't get the definition of "rate of uniform convergence". Hope you can help me!