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Thanks again,
but I found the solution myself by now. \mid does not work, because it is not an extensible character. The correct keyword is \bracevert or \arrowvert, the last one is a little bit thinner. So

\left\lbrace foo \middle\bracevert foo \right\rbrace

does it and results into a correct ...

Thank you,
the scaling works if I use the character | as delimiter, as you suggested. But than the spacing is wrong.
| is the characer for "divides", as in "p|q". Thus it uses a class 2 spacing for binary relations with no space on the left nor right.
Amsmath recommends the \mid keyword, if you need ...

Hello everybody,
I need a way how to make three delimiters (a left, a middle and a right one) having the same size. This situation frequently occurs when defining a set with a vertical bar (\mid) as the "such that" operator.
For example:

\begin{equation}
A = \left \lbrace f \mid foo \right\rbrace ...