In BGP, TCP handles the checksum and BGP does not perform any checksum validation in the application level.
How can we believe TCP must forward the data without errors?
Similarly in RIP with UDP case?
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Allow me to quote Mr. Jeff Doyle
Like EGP, BGP forms a unique, unicast-based connection to each of its BGP-speaking peers. To increase the reliability of the peer connection, BGP uses TCP (port 179) as its underlying delivery mechanism. The update mechanisms of BGP are also somewhat simplified by allowing the TCP layer to handle such duties as acknowledgment, retransmission and sequencing. Because BGP rides on TCP, a separate point to-point connection to each peer must be established.” Jeff Doyle - Routing TCP/IP, Volume II
On the other hand, another routing protocol OSPF rides on IP (protocol #89). OSPF performs its own delivery mechanism utilizing features like LSAcks and a checksum in the packet header.