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When I learned TeX, I was told to not write e.g. something, because TeX would think the period after the “g” ends a sentence, and introduce a wider, inter-sentence space. Instead, I was to write e.g.\␣.

Years later, I learned from a convincing, but since forgotten source, that in fact e.g.\@ is the proper thing to write. I vaguely remembering that e.g.\␣ supposedly affected the inter-word space in some unwanted way. So I did that for many years.

Until I recently was called out for doing it wrong, and that infact e.g.\␣ is the proper way. This was supported by a StackExchange answer written by a LaTeX authority and backed by a reference to documentation. The same question has, however, another answer by another TeX authority, backed by an analysis of the implementation, which concludes that e.g.\@ is proper.

What now? I guess I just have to find it out myself.

The above image shows three variants: The obviously broken version with e.g., and the two contesting variants to fix it. Looks like they yield equal results!

So maybe the difference lies in how \@ and \␣ react when the line length changes, and the word wrapping require differences in the inter-word spacing. Will there be differences? Let’s see;

I cannot see any difference. But the inter-sentence whitespace ate most of the expansion. Is there a difference visible if we have only inter-word spacing in the line?

Again, I see the same behaviour.

Conclusion: It does not matter, but e.g.\␣ is less hassle when using lhs2tex than e.g.\@ (which has to be escaped as e.g.\@@), so the winner is e.g.\␣!

(Unless you put it in a macro, then \@ might be preferable, and it is still needed between a captial letter and a sentence period.)