Showing Tightness of {fn}: A Measurable Approach

[sbashrawi]

Homework Statement

If for each \epsilon>0 , there is ameasurable subset E1 of E that has
finite measure and a \delta>0 such that for each measurable
subset A of E and index n
if m(A\capE1) < \delta , then
\int | fn| <\epsilon ( integration over A)
Show that {fn} is tight

Homework Equations

The Attempt at a Solution

 

[jbunniii]

Show that {fn} is tight

Can you define "tight"?

 

[sbashrawi]

A family F of measurable functions is tight on E if there is a measurable subset E1 of finite measure such that integration of |fn| on ( E-E1) is less than epsilon for each fn in F