Inorganic lead halide perovskites are promising candidates for optoelectronic applications, due to their high photoluminescence quantum yield and narrow emission line widths. Particularly attractive is the possibility to vary the bandgap as a function of the halide composition and the size or shape of the crystals at the nanoscale. Here we present an aberration-corrected scanning transmission electron microscopy (STEM) and monochromated electron energy-loss spectroscopy (EELS) study of extended nanosheets of CsPbBr3. We demonstrate their orthorhombic crystal structure and their lateral termination with Cs-Br planes. The bandgaps are measured from individual nanosheets, avoiding the effect of the size distribution which is present in standard optical spectroscopy techniques. We find an increase of the bandgap starting at thicknesses below 10 nm, confirming the less marked effect of 1D confinement in nanosheets compared to the 3D confinement observed in quantum dots, as predicted by density functional theory calculations and optical spectroscopy data from ensemble measurements.