Time and space must be infinite. Otherwise, there would have to be a definable boundary. When the immense nothingness of truly outer space comes to an end, what is left but nothing... a whole lot of nothing. The fact (or possibility) that there will be no one around to measure infinity - which would be, of course, infinite -, nor will there be anything which will actually traverse all of infinity spatially, is irrelevant. You don't need to arrive at infinity in order to imagine a space-time universe that is just so.