Formally, this theorem holds that (*) "SPACE of little-o of f of n" is a strict subset of "SPACE of f of n".
Geffert extended this theorem to show that there exist unary languages described by this theorem. The original proof of this theorem used a language defined as the set of inputs that a Turing machine does not accept before visiting a certain number of cells. One corollary of this theorem is that L is a strict subset of the class that contains the quantified Boolean formulas problem. One form of it applies to functions f for which there exists a deterministic Turing machine that halts after visiting a number of cells on its tape equal to f of the size of the input. Those functions are constructible in the sense required by this theorem. Formally, this theorem holds that (*) "SPACE of little-o of f of n" is a strict subset of "SPACE of f of n". For 10 points, name this theorem that proves that a Turing machine with access to asymptotically more space can decide more languages.
Geffert extended this theorem to show that there exist unary languages described by this theorem.
space hierarchy theorem [accept (non-)deterministic space hierarchy theorem; prompt on "hierarchy theorem"]