Just create a button element with jQuery, and add the event handler when you create it :
var div = $('', {'data-role' : 'fieldcontain'}),
btn = $('', {
type : 'button',
value : 'Dynamic Button',
id : 'btn_a',
on : {
click: function() {
alert ( this.value );
}
}
});
div.append(btn).appendTo( $('#pg_menu_content').empty() );
FIDDLE