THE RELATION BETWEEN SSC(F, K) AND Q(M) CONDITIONS

Let be some family of curves in A nonnegative Borel function is called the admissibility metric of the family if for every . The modulus of the family is defined by the formula where inf is taken over the class of all possible metrics . For a pair of continums the symbol denotes the modulus of the family of all curves in connecting and . The direction of the square will be called an angle such that when turning to an angle , the square is transformed into a square whose sides are parallel to the coordinate axes.

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