Measures for oscillatory sequences

The classical concept of oscillation is not sufficient to fully describe the oscillatory behavior of a real sequence. By introducing the concepts of frequency measures of subsets of integers, and investigating their properties, we are able to strengthen the original concept of an oscillatory sequence and thus new oscillation criteria for difference equations can be derived. These criteria differ from the classical ones in that they are described by means of the measures of the level sets of the involved parameter sequences. A brief description of the theory of frequency measures for multiple sequences is also given.