Questions tagged [signed-measures]

A signed measure is a countably additive set function on a sigma-algebra and taking values in the extended reals, but not permitted to assign negative infinity to a set.

The idea of signed measure is an extension of the measure of . A signed measure also is a function with domain of definition a given sigma-algebra of sets, but is more general than ordinary measure in that the value assigned to a set may be a negative real number.

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Find signed measure and Hahn decomposition

For which $p\in\Bbb{R}$ exists a signed measure $\mu$ on [0,1] with the sigma-algebra of the Borel sets with $\mu([0,x])=f(x):=x^psin(1/x)$. Find a Hahn decomposition for $\mu$. I find the part with $p$ quite difficult but the Hahn decomposition I…
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