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$$\cap$$E1) < $$\delta$$ , 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