Definition of Measure regular

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Book's, Real and complex analysis, Walter Rudin.

I am somewhat confused.

My question is:

"In other words, we are looking at $L^p$, where $\mu$ is Lebesgue measure on $[0,2\pi]$(or on $T$), divided by $2\pi$".

The (Lebesgue) measure in $[0,2 \pi]$ is the same as $T$?

Thank you all.