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Jan 9, 2018 at 19:02 comment added mohi Thank you for your response. Yes I agree with your statement. However, please note that we now only have a one sided bound on f in the assumption rather than the two sided version. so one can not conclude the second identity from the first one due to the different assumptions.
Jan 8, 2018 at 18:46 comment added Nikolayevich I might get something wrong, but isn't your second probability upper-bounded by your first probability? Apparently inf a_n <-t => sup |a_n| > t
Aug 2, 2016 at 18:27 history asked mohi CC BY-SA 3.0