What is "my" doing here? I don't understand.

Using "my" is the same as saying "that I...", "the fact that I...".

Other examples :
http://tatoeba.org/sentences/se...o+you+mind+my"

Saying "Do you mind my turning on TV?" is the same as saying "Do you mind that I turn on the TV?"

Maybe there's a "the" missing.
=> Do you mind my turning on the TV?
An English speaker will have to confirm that.

Ahh now I understand, nevertheless I think "me" should go there rather than "my": "Do you mind me turning on the tv?"

English speaker here.

Do you mind my turning on TV?
Do you mind that I turn on the TV?
Do you mind me turning on the tv?

All three are correct.

To answer why "my" is fine, note that the word "turning" is a gerund, i.e, a noun.

Hope that helps.

Thank you.

There is a difference between "Do you mind turning on TV" and
"Do you mind my turning on TV"
"Do you mind turning on TV" is a request.It means: "Will you turn on TV?"
"Do you mind my turning on TV" is a permission. It means: "May I turn on TV."

I've unlinked the Japanese that doesn't match this change.

Do you mind turning on the TV?
edited by Nolantm, April 7, 2009

テレビをつけても構いませんか。