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Feb 23, 2021 at 22:47 comment added MikeG Thanks a lot!!!
Feb 23, 2021 at 17:56 comment added Jochen Glueck @MikeG: I've added more details to the proof, as well as several remarks and references after the proof.
Feb 23, 2021 at 17:55 history edited Jochen Glueck CC BY-SA 4.0
Added many detailed and further references.
Feb 23, 2021 at 15:02 comment added MikeG More details of the second is highly welcomed! actually I am new to functional analysis and don't know what is mean ergodic projection and how it works here...or maybe some suggested materials for me to work out it by myself?
Feb 23, 2021 at 14:59 vote accept MikeG
Feb 23, 2021 at 13:12 history answered Jochen Glueck CC BY-SA 4.0