Raz Paralel pretition teorema adalah hasil yang penting dalam PCP, inapproximation, dll Teorema ini fomalized sebagai berikut.
My quesion is what happen if the sets are infinite, in a continuous space. Say if are subsets of a space, say , or more abstract spaces. All the rest are same. Raz's theorem only gives a trivial upper bound since the sizes of answer sets are infinite. Obviously -fold value is upper bounded by single copy. Does exponential decrease also happen in continuous case? Would it be more interesting to restrict to be collections of continuous functions or functions or measureable functions?