Should Aggregate Functions always return one row?

Hello.

Is this a bug?

linux=# SELECT * FROM test;
x
---
1
2
3
(3 Rows)

linux=# SELECT * FROM test WHERE FALSE;
x
---
(0 Rows)

phlegma=# SELECT max(x) FROM test WHERE FALSE;
max
-----

(1 Rows)

phlegma=#

So, if I use the max() aggregate, I receive one row with the value NULL. Is
that correct?

My background is the language plpgsql:

I expected to test for the existance of a maximum with
(...)
SELECT INTO e
max( y ) AS x FROM (table) WHERE (condition);

IF NOT FOUND THEN RETURN; END IF;
(...)

But I have to test with:

(...)
SELECT INTO e
max( y ) AS x FROM (table) WHERE (condition);

IF e.x IS NULL THEN RETURN; END IF;
(...)

Thanks in advance,
Wilhelm