Okay so if D = (x_0,...,x_m) a division of the interval [a,b], denote
V(f,D) = sum_(i=i..m) |f(x_i) - f(x_(i-1))|.
And:
V(f_n,D) <= V(f_n) ==>
Then:
liminf_n V(f_n,D) <= liminf_n V(f_n)
But, liminf_n V(f_n,D) = lim_n V(f_n,D) = V(f,D).
Hence V(f,D) <= liminf_n V(f_n), for each D, ==>
V(f) <= liminf_n V(f_n).
Then what is "D"!??
MacGyver PLEASE HELP! All I have to work with is an elastic band, a paperclip, a small piece of string and a pen lid. Save me Macgyver, you're my only hope!
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Pet Sounds
By The Beach Boys
Release date: 13 July, 1999 |
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