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This proceeding reports the ATLAS results of measuring vector bosonproduction in $pp$ and $p$+Pb collisions at the center-of-mass energy of5.02~TeV per nucleon. $Z$ boson bosons are reconstructed via leptonic decaysand results are presented as a function of $Z$-boson rapidity. $W$ boson bosonsare identified by measuring leptons coming from $W$ boson decays and theresults are presented as a function of lepton pseudorapidity. In $pp$collisions $Z$ boson boson cross section in $|y_{Z}|<2.5$ is 590$\pm$9(stat.)$\pm$12 (syst.)$\pm$32 (lumi.) pb. In $p$+Pb system kinematicdistributions of $W$ boson and $Z$ boson bosons are compared to models based onNLO and NNLO QCD calculations using different PDF sets. Using PDF modificationshows better agreement of the model and the data. Measurements done indifferent centrality intervals show that the PDF modification in $p$+Pb mayhave centrality dependence.

$W$ and $Z$ boson production in 5.02 TeV $pp$ and $p$+Pb collisions with the ATLAS detector