For simplicity, we can consider all these numbers as 4-digits numbers, by writing leading 0 (zero, or zeroes) to

all one-digit, two-digit and three-digit numbers.


We only need to subtract from this set the number  0 = "0000" at the end, since it is not positive number.


Now we can easy count all such numbers from 0 to 2000:

    fixed 0 in the most left position;

    any of 5 digits 0, 2, 4, 6, 8 in the hundreds position;

    any of 5 digits 0, 2, 4, 6, 8 in the tens position;

    any of 5 digits 0, 2, 4, 6, 8 in the ones position.


In all, there are  5*5*5 = 125 numbers, so far.


Subtract  "0000" from this set to get 125 - 1 = 124 numbers.


Add 6 numbers 2000, 2002, 2004, 2006, 2008, and you will find the final answer: 124 + 5 = 129 numbers.


ANSWER.  129 numbers.