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## Homework Statement

Let 1

_{A}stand for an indicator function and

Let fn = 1

_{{n}}and gn={1

_{{1}}n odd, 1

_{{1}}n even.

Find lim

_{n->∞}sup{fn} and limsup

_{n->∞}{gn}

## Homework Equations

## The Attempt at a Solution

The limits are pointwise so I found given x, then

lim

_{n->∞}sup{fn} = 0

limsup

_{n->∞}{gn} = {1 for x=1 or x=2 and 0 elsewhere}

Do you agree? I just wanted to check basically :)