The Standardized Treatment Of Hausdorff Measure

This paper mainly studies the contact between revised Hausdorff standardized measure and Lebesgue measure on arbitrary hyperplane,and shows the ralationship between h k( F )and Lk ( F ) in diffrenet conditions. First, given the meaning of the universal and generalized ball-cover, and then introduced the definition of the universal and generalized ball-cover Lebesgue measure and ball-cover Hausdorff measure.Proposed the definition of non-zero nature of countable cover,and unified the definitions of Hausdorff measure with the dimension equal to zero and over zero. Further introduced standard and reduction the definition of ball and ball cover by the s-dimensional volume, definition of the ball-cover revised Hausdorff standardized measure,and unified the definitions of ball-cover Lebesgue measure and ball-cover Hausdorff measure.Then amend Hausdorff standardized measure to make it consistent with Lebesgue measure on arbitrary hyperplane.