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 Jan 27 awarded Popular Question Dec 4 awarded Notable Question Oct 30 awarded Popular Question Sep 11 awarded Nice Question Jul 2 awarded Curious May 30 awarded Yearling Jan 28 awarded Notable Question Jul 31 awarded Popular Question Jul 5 awarded Nice Question Jul 9 awarded Nice Question Apr 25 awarded Popular Question Jan 5 awarded Yearling Apr 4 accepted Form of the inner product in $\ l_2$ Mar 31 comment Sequence of subspaces of $\ [ 0,2{\pi} ]$ with length that goes to $\ 0$ @Alexander Thumm Or i can use the final answer without $\ 2^n$ but just $\ n$ in the denominator.In this way the division of $\ [0,2 {\pi} ]$ is more smooth. Mar 25 comment Sequence of subspaces of $\ [ 0,2{\pi} ]$ with length that goes to $\ 0$ Thank you for your time Mar 25 accepted Sequence of subspaces of $\ [ 0,2{\pi} ]$ with length that goes to $\ 0$ Mar 25 comment Sequence of subspaces of $\ [ 0,2{\pi} ]$ with length that goes to $\ 0$ @Alexander Thumm I edited the question because it was not going to solve my problem(see comments under my question).My mistake Mar 25 revised Sequence of subspaces of $\ [ 0,2{\pi} ]$ with length that goes to $\ 0$ added 67 characters in body Mar 25 comment Sequence of subspaces of $\ [ 0,2{\pi} ]$ with length that goes to $\ 0$ For each x it is a sequence of numbers so the usual topology of R.I ws thinking F_n be everywhere 0 exept an interval of lenght that goes to 0 where say f_n =1.But i need at every x an oscillation between 0 and 1.That's why i need this sequence. Mar 25 comment Sequence of subspaces of $\ [ 0,2{\pi} ]$ with length that goes to $\ 0$ I think it can solve a problem of Stein,Fourier analysis(a collegue of mine thought it is a nice problem and gave it me-but i dont know fourier analysis!).So with elementary knowledge i was trying to find a sequence of functions that the integral of their squares tend to 0 but the f_n(x) does not converge at no x.