Skip to main content
Bumped by Community user
Bumped by Community user
Bumped by Community user
Bumped by Community user
Bumped by Community user
Bumped by Community user
Bumped by Community user
edited tags
Link
Source Link

Decomposition of non negative Radon measure into $L^1$ and $H^{-1}$ functions

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 $H_0^1$).