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The cosmic microwave background radiation provides unique constraints oncosmological models. In this Letter we present a summary of the spatialproperties of the cosmic microwave background radiation based on the full 4years of COBE DMR observations, as detailed in a set of companion Letters. Theanisotropy is consistent with a scale-invariant power law model and Gaussianstatistics. With full use of the multi-frequency 4-year DMR data, including ourestimate of the effects of Galactic emission, we find a power-law spectralindex of $n=1.2\pm 0.3$ and a quadrupole normalization$Q_{rms-PS}=15.3^{+3.8}_{-2.8}$ $\mu$K. For $n=1$ the best-fit normalization is$Q_{rms-PS}\vert_{n=1}=18\pm 1.6$ $\mu$K. These values are consistent with bothour previous 1-year and 2-year results. The results include use of the $\ell=2$quadrupole term; exclusion of this term gives consistent results, but withlarger uncertainties. The 4-year sky maps, presented in this Letter, portray anaccurate overall visual impression of the anisotropy since the signal-to-noiseratio is ~2 per 10 degree sky map patch. The improved signal-to-noise ratio ofthe 4-year maps also allows for improvements in Galactic modeling and limits onnon-Gaussian statistics.Comment: 11 pages plus 2 PostScript figures. Figures 2 and 4 are not included,  but are available upon request to bennett@stars.gsfc.nasa.gov. Submitted to  The Astrophysical Journal (Letters

Four-Year [ITAL]COBE[/ITAL] DMR Cosmic Microwave Background Observations: Maps and Basic Results