Some Properties Of Measure Frames

Measure frames is a kind of measures which have the completely compact supports and they also can be a generalization of the vector frames in Hilbert spaces.In this paper,we generalize the construction of vector frames to the measure frame case by using the properties of discrete and continuous frames.Our study includes the investigation on canonical dual and pseudo dual,the sum of two measure frames,the dilation of a measure frame and the disturbance.We also discuss some equalities and inequalities about measure frames.At last,We research the disjointness and dual for the sub-measure frames.