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Then SV a b ( F ) is said to be the semi-variation of F on [ a, b ] (cf. e.g. [17]).b It is clear that if F ∈ BV ( [ a, b ], L ( X ) ) then F has bounded semi-variation on [ a, b ] while the reversed implication is not true in general (cf. [[18], Theorem 2]).
Similar(59)
The reverse implication is obvious.
Similarly, the reverse implication follows.
The reverse implication is an open problem.
The reverse implication is not in general true.
The reverse implication is not true (see, [8, Example 2.1]).
For the reverse implication, we use the same technique.
The reverse implication does not hold, in general.
For the reverse implication, we use the same strategy.
The reverse implication follows from the above lemma.
In it we use \ \Leftarrow\) for reverse implication.
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