I don't believe there is any true way to measure the distance between two vertices in the uv image editor, but there is a fairly simple workaround.
Finding the (x,y) distance between two points
With your mesh unwrapped and the UV/image editor open, open the properties panel within the editor via n. At the top there will be what is called "UV vertex". Once you select a vertex it will tell you the coordinates of the vertex.[![Selected Vertex][1]][1]
Okay, now the hard part. After finding the coordinates of the second vertex use the distance formula, which is: √ (x2−x1)2+(y2−y1)2
This online distance caculator should make things easier.
Duplicating a UV island
*In 3D View*First and foremost you must select the desired UV island, like so:
1. Enter edit mode TAB
2. Put select mode on "face" CTRL+TAB
3. Hover mouse over the desired UV island and press L.
4. Hit Shift+D
*In UV/Image Editor*
Whatever you copy and paste in 3-D view should appear in the image editor.