frequency ranges for which PLL can achieve lock, were introduced. They are widely used nowadays (see, e.g. contemporary engineering literature and other publications). Usually in engineering literature only non-strict definitions are given for these concepts. Many years of using definitions based on the above concepts has led to the advice given in a handbook on synchronization and communications, namely to check the definitions carefully before using them. Later some rigorous mathematical definitions were given in.

Gardner problem on the lock-in range definition