TITLE: How helpful is non-standard analysis?
QUESTION [60 upvotes]: So, I can understand how non-standard analysis is better than standard analysis in that some proofs become simplified, and infinitesimals are somehow more intuitive to grasp than epsilon-delta arguments (both these points are debatable).  
However, although many theorems have been proven by non-standard analysis and transferred via the transfer principle, as far as I know all of these results were already known to be true.  So, my question is: 
Is there an example of a result that was first proved using non-standard analysis?  To wit, is non-standard analysis actually useful for proving new theorems?
Edit: Due to overwhelming support of Francois' comment, I've changed the title of the question accordingly.

REPLY [7 votes]: I just came across a 2013 book by F. Herzberg entitled "Stochastic Calculus with Infinitesimals", see http://link.springer.com/book/10.1007/978-3-642-33149-7/page/1 where probability and stochastic analysis are done without having to develop the complexities of measure and integration theory first.  Ever since E.Nelson, such an approach is called "radically elementary" and it really is.  What this proves is the new result that stochastic calculus can be done without measure theory.  
To give a historical parallel, recall that Leibniz's mentor in mathematics was Huygens.  When Huygens first learned of Leibniz's invention of infinitesimal calculus, Huygens was sceptical, and wrote to Leibniz that he is merely doing what Fermat and others have done before him in a different language.  What Huygens failed to recognize immediately (but did recognize later) was the generality of the methods and the lucidity of the presentation of Leibniz's new approach.  The Nelson-Herzberg approach to stochastic calculus is in a way more significant than merely a new "result", since it provides a new methodology.