Is the xml:lang attribute required (in addition to the HTML lang attribute) when specifying the language of an XHTML element?

I've got an XHTML 1.0 Transitional document. Most of the content is in English, hence this is what I've got at the top:

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">

<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">

Some elements are in different languages, e.g.

<a href="#" lang="es">Español</a>

Do I need to add xml:lang="es" to elements like these as well, thus duplicating the language information?

Solution

If you're sending the file with the text/html MIME type, you should, because you're trying to use both HTML and XHTML. (Browsers will only look at the lang, though.)

If you're using the correct MIME type (application/xhtml+xml), on the other hand, only xml:lang="" is necessary, if (correctly) pointing out that you're using HTML, with an HTML doctype, you just need lang="".