wrong. he shouldn't exist because nothing says he does.
Nothing used to say the atoms existed, but they did. For something to exist, someone doesn't necessarily have to have said it does.
we can measure all measurable things and conclude that there is no reason for God to exist.
And God is unmeasurable... I don't get where you're going with this. If something exists outside the Universe, we can't measure it.
Do you understand my argument at all? Outside of the Universe ANYTHING could exist. We will never know what actually exists, because we can't measure it. There being some proof inside our Universe that such an object exists would be impossible, because we can't measure these things. This means that and infinite amount of things could exist outside of the Universe. One of such things could be God, another could be a tennis ball etc. Equally, there could be nothing. We'll never know either way, so being Atheist and saying that there definitely isn't a God is in effect saying that you believe there to be nothing outside of the Universe. Again, this is a possibility, but the probabilities are the same. Therefore, Agnosticism is the only logical option. To accept we will never know what is outside of our Universe and that it isn't worth our time considering it.