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I've just begun studying measure theory , and i cant help it but to think of it in terms of probability theory , i don't know if that is right or wring . any way , i have this naive question :

consider the following : we have n sample spaces [tex]\Omega_{}i[/tex], each with a distribution P[tex]_{}i[/tex] ( i=1,...n) , if we combine (union) the sample spaces to form a new sample space whose distribution is unknown , is there a way to extract the distribution of the new sample space from the previously know distributions ??