This is an announcement for the paper "The generalized Busemann-Petty problem with weights" by Rubin Boris. Abstract: The generalized Busemann-Petty problem asks whether origin-symmetric convex bodies with lower-dimensional smaller sections necessarily have smaller volume. We study the weighted version of this problem corresponding to the physical situation when bodies are endowed with mass distribution and the relevant sections are measured with attenuation. Archive classification: Functional Analysis Mathematics Subject Classification: 52A38; 44A12 Remarks: 12 pages The source file(s), sol1.tex: 32080 bytes, is(are) stored in gzipped form as 0505666.gz with size 11kb. The corresponding postcript file has gzipped size 57kb. Submitted from: borisr@math.lsu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0505666 or http://arXiv.org/abs/math.FA/0505666 or by email in unzipped form by transmitting an empty message with subject line uget 0505666 or in gzipped form by using subject line get 0505666 to: math@arXiv.org.