[jQuery] Select part of text and add a CSS class

Hi,
I am trying to create my first jQuery script. I want to have a text in
a <p>, select it with the cursor and add a class to it. I know that I
can use the .select and .addClass functions.

$("p").live("mouseup",
        function() {
                selection = getSelectedText();
                if(selection.length >= 3) {
                        $(this).html($(this).html().addClass("selected");
                }
        }
);

//Grab selected text
function getSelectedText(){
    if(window.getSelection){
                return window.getSelection().toString();
    }
    else if(document.getSelection){
        return document.getSelection();
    }
    else if(document.selection){

        return document.selection.createRange().text;
    }
}

I can not get this to work.
Thank you.