Your menu_function() is NOT just firing an alert test message - it is adding a live click listener to everything in the DOM that has a class of "select_li" that fires a test alert. This means that every time you click on #menu you are adding ANOTHER listener to .select_li - so if you click #menu 10x, you should have 10 listeners for each click of .select_li.
If you are truly trying to JUST show an alert when you click on #menu, your menu_function() should only look like this:
function menu_function() {
alert("test");
}