Understanding Normalized Lebesgue Measure on the Unit Circle

[LikeMath]

What do we meen by "Normalize Lebesgue Measure", when we talk about functions on the unit circle.
If some example is introduced it will be better (how to evalutae the integral).

 

[mathman]

What do we meen by "Normalize Lebesgue Measure", when we talk about functions on the unit circle.
If some example is introduced it will be better (how to evalutae the integral).

"normalize" is typically to convert measure into probability by dividing integrals, etc. by the total measure, in this case π. Evaluation of an integral isn't affected otherwise.

 

[LikeMath]

Ok. Thank you, but my second question is "could you please give me a function in Hilbert Hardy space and find its norm? "

 

[mathman]

I am not familiar with this space. I looked it up on Wikipedia. Any constant C will answer your question. The norm will be |C|.