Reinitializing jquery event on ajax response

I had a jquery change event attached to a checkbox which was part of a div.

<div id="test-div">
<input type="checkbox" checked="checked" value="1" class="test-chkbox" />
</div>

Using the following JQuery code a change event was attached to the above check-box

$(".test-chkbox").change(function () {
    $.ajax({
        type: "GET",
        url: "some-action",
        data: this.value,
        cache: false,
        success: function(response) {
            $("#test-div").replaceWith(response);
        }
    });
});

Response of ajax contained the same check-box but the change event was no more attached to it, so to solve the issue I changed jQuery code as specified below.

$(document).on("change", ".test-chkbox", function () {
    $.ajax({
        type: "GET",
        url: "some-action",
        data: this.value,
        cache: false,
        success: function(response) {
            $("#test-div").replaceWith(response);
        }
    });
});

The above change made sure that the change event is always attached to check-box even after the ajax response.

Note: Older versions of jQuery use .delegate and .live instead of .on