They are all correct in AmE.
One form is possessive adjective + gerund noun. The other form is objective pronoun + participle.
Interested in Language
Hi, respectable teachers,
When I checked with google:
【We appreciate your being here.】is way more than【We appreciate you being here.】
【We appreciate you helping us.】is more than【We appreciate your helping us.】
Do you think 4 sentences are all correct? Do they all sound natural to native speakers?
(Please specify it's AmEnglish or BrEnglish, if it is proper)
Thank you very much!
Thank you Rover_KE,
especially for your correction of my questions!!
That's very nice of you!
Thank you, you guys!
WR and UE forums without making the amendments I had suggested.
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***** NOT A TEACHER *****
The teachers have already answered you. I just wanted to share some ideas that, I believe, are reasonably accurate.
1. Here in the United States, I suspect that most people who say "I appreciate you being here" ACTUALLY mean "your." Most people, of course, are very busy with their lives and have no time (or interest) in the finer points of grammar. Since so many people (of all educational levels) say "you," it is understandable that many (most?) Americans use "you" without thinking about it.
2. There are some (a few?) people who feel that there is a helpful distinction between the two. I will discuss what they say. I am not saying that they are correct, especially in 2015, when some grammar "rules" are no longer followed by many native speakers.
a. "I really appreciate your being here." = The emphasis is on the "being." You did not know whether you would have time to attend the speaker's party, but you rearranged your work schedule in order to attend the party. The speaker wants to express his gratitude.
b. "I really appreciate you being here." = The emphasis is on "you." Let's say that you and the speaker were once friends but later became enemies. Yet you show up at the speaker's birthday party. The speaker is astonished, grateful, and touched that you (an enemy) would actually come to her birthday party!
3. I personally like this distinction, but I doubt that many people nowadays follow it.