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rigliztetbf 2022-06-27 Answered
Show that f ( x ) = n = 0 a n x n , for x [ 0 , 1 ], is of bounded variation
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Answers (1)

Harold Cantrell
Answered 2022-06-28 Author has 21 answers
Let
0 = x 0 < < x n = 1 ,
then
k = 1 n | f ( x k ) f ( x k 1 ) | = k = 1 n | j = 0 a j x k j j = 0 a j x k 1 j | k = 1 n j = 0 | a j | ( x k j x k 1 j ) = j = 0 | a j | k = 1 n ( x k j x k 1 j ) = j = 0 | a j | < .
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