I noticed that many people sometimes omit the definite article before "Lebesgue measure". Some examples: "suppose that m is Lebesgue measure on R, "we will construct Lebesgue measure on R", etc. This looks odd to me and in both cases I would have written "the Lebesgue measure" and I see that, for instance, this is how Rudin expresses himself in his classic text (at least in some places, he seems to use both of these variants).
My question is whether the article should be omitted here or whether it is a matter of personal taste.

  • I think the article would be usual.
    – mdewey
    Commented Dec 28, 2021 at 11:49
  • @mdewey thanks, but then why do so many authors omit it? I guess that both are correct, but the article feels more natural.
    – MathIsCool
    Commented Dec 28, 2021 at 12:12
  • I did a bit of searching to see where the article-less form occurs. Typical seems to be this: The collection M is the Lebesgue σ-algebra of R, and m is Lebesgue measure on R. The elements of M are known as the Lebesgue measurable sets in R. When there are that many articles kicking ariound in the vicinity, it's forgivable to discard one now and then! I also get the impression a lot of the relevant "science-based" writers aren't native Anglophones anyway. Commented Dec 28, 2021 at 12:27
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    I wouldn't say it's "all right", no (it's never correct to drop the article before a noun phrase like this). So don't bother trying to learn some obscure principle whereby sometimes it might be "more excusable" to omit the article. Just do it the right way yourself every time, and don't take any notice of others (native Anglophones or not) who get it wrong. Commented Dec 28, 2021 at 12:38
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    @FumbleFingers I agree with you, thank you very much for taking the time to look into this.
    – MathIsCool
    Commented Dec 28, 2021 at 12:54

1 Answer 1


Assuming there is only one Lebesgue measure, the "the Lebesgue measure" would be correct, and you should not drop the definite article.

If there are many different measures then you could say "a Lebesgue measure".

In either case you shouldn't omit the article, as the mathematical sense of "measure" is countable.

  • thank you very much! There is indeed only one Lebesgue measure and this is a well known result in maths. I am really glad that people also answer such technical questions here, it is a bit difficult for a non-native to learn technical vocabulary and wording, lucky for me there are such great forums nowadays!
    – MathIsCool
    Commented Dec 28, 2021 at 22:15

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