That is what I meant - I am more asking for a solid philosophical interpretation than a mathematical theory, after all frequentism, Bayesianism and all the othe

That is what I meant - I am more asking for a solid philosophical interpretation than a mathematical theory, after all frequentism, Bayesianism and all the other interpretations seem to carry quite a bit of philosophy. On the other hand in another comment it just boiled down to the question whether there is a measure that gives 1 for the set of all infinite binary sequences with 50/50 zeros and ones and 0 for the set of all the other sequences. So it is not pure philosophy what I am interested in.