This shows up a lot behind fridges it is most likely mold. I have had a couple who have had it tested and it came back just a common mold that can be cleaned. But that does't mean that that is what yours is. Personally I would scrub it with bleach water let it totally dry and go on. I don't know if then putting a moldicide in your paint will help or not. You could pull the fridge out say once a month and wash the area with a weak bleach solution and maybe keep it from happening.
The picture shows what looks like a bunch of small independent mold colonies. Most likely caused by a lack of airflow, and a supply of dust to feed on. A wipedown with a fungicide will take care of it. Something like Tilex or Lestoil will fix it in short order. Pulling the fridge out and wiping down the wall occaisionally will prevent them from growing from colonies into thier own third world country.
The refrigerator is a moisture source when they condense the water vapor as part of the cycle, bound to get some on the wall. Check under/behind for lint/dirt build-up on the coils.... use a flashlight---- when wife is not around.OR, while cleaning, announce- "It was time for the annual cleaning under there".
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