Is the languague L={, M accepts a finite amount of words} decdidable?
The function you defined is not a reduction at all - it may not even stop!
The problem is running $m$ on $w$: can you be sure $m$ wont be stuck in an infinite loop on $w$? you can't.
You can define a proper reduction as follows: (on input $&lt;m,w&gt;$)
Create the machine $M_{m,w}$that does the following algorithm, and return in: (on input $s$)

Emulate $m$ on $w$ for $|s|$ steps. If $m$ halted in that time, reject $s$. Otherwise, accept $s$.

I will leave it for you to prove this is a proper reduction from $H_{TM}$ to $L$ (its a good exercise!)