  We introduce the Integrated Dual Local Depth which is a local depth measure
for data in a Banach space based on the use of one-dimensional projections. The
properties of a depth measure are analyzed under this setting and a proper
definition of local symmetry is given. Moreover, strong consistency results for
the local depth and also for the local depth regions are attained. Finally,
applications to descriptive data analysis and classification are analyzed,
making the special focus on multivariate functional data, where we obtain very
promising results.
