javascript: Check inputs for empty strings

FormValidation.html

<form action="#action" method="get">
  <label For="FirstName">First Name*</Label>				
  <input id="FirstName" Type="text" Name="FirstName" class="required" data-message="Please fill in First name"/>
  <label For="LastName">Last Name*</Label>
  <input id="LastName" name="LastName" class="required"  data-message="Please fill in Last name"/>
  <input Type="submit" name="send" />		
</form>

jquery.require-field.js

(function($, undefined){	
			// cache form 		
			var theForm = $('form');		
			/**
			Xbrowser trim function
			@function trim
			@parameter {string} str		
			**/
			var trim = function(str) {
				str = str.replace(/^\s+/, '');
				for (var i = str.length - 1; i >= 0; i--) {
					if (/\S/.test(str.charAt(i))) {
						str = str.substring(0, i + 1);
						break;
					}
				}
				return str;
			};
			/** 
			Function to check for empty form values 
			@function validateForm
			@parameter {object} e			
			**/
			var validateForm = function(e){
				var invalid = [];
				var message = "";
				// find required fields
				var requiredFields = theForm.find('.required');	
				// check that field values are not empty
				requiredFields.each(function(){
					var $elem = $(this);								
					// check curren elem value for empty string
					var value = trim($elem.val());
					if(value === ""){
						e.preventDefault();								
						e.stopPropagation();						
						// push to invalid array
						invalid.push($elem);
					}
				});	
				if (invalid.length){
					// Build single message from each invalid message
					$.each(invalid, function(){
						message = message + this.attr('data-message') + '\n';
					});
					// notify user
					alert(message);					
				}				
			};			
			// bind validate function to form submit event
			theForm.bind('submit', validateForm);

		})(jQuery);