Memory hard function (MHF) is a class of functions where the majority of the cost of their evaluation comes from the fact that they take a significant amount of memory. It is different from memory bound functions, the latter incurs cost by slowing down computation through memory latency. It finds its use as a form of proof-of-work.
Memory hard measure
There are different ways to measure the memory hardness of a function. A commonly seen measure is Cumulative Memory Complexity.