For the width of the border you need to specify the side of the border. borderWidth / border-width is a shortcut to all border-width once.
$( function() { alert($('div').css("border-top-width")); });
http://jsfiddle.net/ZsSmp/
In addition, you need to specify more frame widths so that it is valid. Just specifying a width border does not create a border. To do this, you need color and style:
border: 2px solid black;
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