I don't remember a lot of things

[navi tasan]

Is this sentence ambiguous:
1-"I don't remember a lot of things that happened on that day."

I think it could mean:
a-It is not true that I remember a lot of things that happened on that day, or to put it more naturally: I don't remember much of what happened on that day.
Or:
b-There are a lot of things that happened on that day which I do not remember.
b does not actually contradict "I remember a lot of things that happened on that day." It could be that there were a lot of things that happened on that day which I do remember and a lot of things that happened which I do not remember.
Am I correct or am I off the track?
I think in spoken English the two meanings can be distinguished by the way the sentence is pronounced:
1-I DON'T remember a lot of things that happened on that day.
1b-I don't remember A LOT of things that happened on that day.

[Tdol]

With the pronuciation stress, you could see those meanings. If the sentence were cold on the page, I wouldn't take it as meaning 'I don't remember much..' because the speaker\writer hs chosen an unusual form deliberately. I would naturally take it as ma#eaning that a lot happened which he or she remembers, but equally a lot has slipped their memory. :o

[navi tasan]

Thanks TDOL.
I suppose the same goes for:
1-"I don't remember a lot that happened that night."
and
2-"I don't remember a lot of what happened that night."

[Tdol]

I'd say so.