In this contribution we discuss the main outcomes of our studies on the so called double parton distribution functions (dPDFs), accessible quantities in high energy proton-proton and proton nucleus collisions, in double parton scattering processes (DPS). These new distributions are almost unknown, nevertheless they encode information on how partons inside a proton are correlated among each other. Double PDFs represent a new tool to explore the three dimensional partonic structure of hadrons. Here, we show results obtained from calculations of dPFDs. In particular we focus our attention on the impact of double correlations in experimental observables by showing how the latter could be studied in the next LHC run. We also discuss how the present knowledge on a peculiar experimental observable could unveil new information on the transverse
proton structure.