I Want 4 Digits, But Can You Repeat Some?

We will first consider the number of 4-digit integers that have no digits repeated. Note that we have $9$ choices for the thousands digit, $9$ choices for the hundreds digit (as we can't repeat the first number, and we can now choose 0) $8$ choices for the tens digit and $7$ choices for the units digit. So the number of 4-digit numbers in which all digits are different is $9\times 9\times 8\times 7=4536.$

Since there are 9000 4-digit integers, the number of these that have at least one digit repeated is $9000-4536=\boxed { 4464 } .$