Distributions of event-by-event fluctua tions of the me an transverse mome ntum and me an  transverse energy nearmid-rapidity have been measured in Au+Au c ollisions at roots(NN)=130 GeV at the R elativistic Heavy-Ion Collider. By comparing the d istributions to what is expected for statistically inde pendent particle emission, the m agnitude of non statistical fluctua tions in me an transverse mome ntum is determined to be consistent with zero. Also, no significant nonr andom fluctua tions in me an transverse energy are observed. By constructing a fluctua tion mode l with two event classes that preserve the me an and variance of the s emi-inclusive p(T) or e(T) spectra, we exclude a r egion of fluctua tions in root s(NN)=130 GeV Au+Au collisions.