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What is a reference for the following result (which appears to be well-known in measure theory)?

Any non negative Radon measure can be decomposed uniquely into the sum of an absolutely continuous measure and a singular term with respect to the harmonic capacity. The absolute continuous term itself can be decomposed (not uniquely) to a function in $L^1$ and a function in $H^{-1}$ (dual of $H_0^1$).

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  • $\begingroup$ Can you point to some work where this result is used? Are the three decomposed parts again non-negative? $\endgroup$
    – gerw
    Commented Jul 13, 2021 at 11:43

1 Answer 1

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You can find both results in Theorems 2.1 and 2.4 in

Lucio Boccardo, Thierry Gallouët, Luigi Orsina,

Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data,

Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Volume 13, Issue 5, 1996, https://doi.org/10.1016/S0294-1449(16)30113-5.

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