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I have the Example environment as a new theorem environment but I need to break the example across the article. Ideally I would like to implement the following:

Example 1. blah blah blah ...

... more text form the article ...

Example 1 (continued). other blah blah blah

I tried to define a newtheorem* environment \newtheorem*{ex1}{Example 1} but then I lose the bold part and the "continued" does not appear in parenthesis:

Example 1. continued

I was thinking the perhaps re-setting the counter manually before and after would solve it. But is this possible? Is there some better solution?

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In your particular case it might be easiest to do this:

    \newtheorem{example}{Example}
    \newtheorem{examplecontinued}[example]{\addtocounter{example}{-1}Example}

And then write

    \begin {example} 
    Lorem ipsum
    \end{example}

    \begin{examplecontinued}[continued]
    continued lorem ipsum
    \end{examplecontinued}

This will allow multiple breaks as well. If you want to, you can also define the examplecontinued-environment to automatically display "(continued)" behind "Example [counter] ". How to do stuff like that is very well described in the amsthm-documentation.

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