Locally integrable functions play a prominent role in functions of bounded variation.
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BD is a strictly larger space than the space BV of functions of bounded variation.
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By using his results, it is easy to prove that functions of bounded variation form an variable.
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For example, if a function has bounded variation then its Fourier series converges everywhere to the local average of the function.
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A function " g " is of bounded variation if and only if it is the difference between two monotone functions.
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The same therefore applies to an arbitrary bounded linear form ?, so that a function ? of bounded variation may be defined by
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Functions of bounded variation have been studied in connection with the set of function of bounded variation on an interval [ a, b ] then
8.
Functions of bounded variation have been studied in connection with the set of function of bounded variation on an interval [ a, b ] then
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Where the control, the continuous path X _ t taking values in a Banach space, need not be differentiable nor of bounded variation.
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One of the most important aspects of functions of bounded variation is that they form an ordinary and partial differential equations in mathematics, physics and engineering.
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