Mr. Bloomberg's procedure occurred before he was a candidate for mayor, and aides say questions about his health did not come up as he ran for office.

But he has now reached a level of prominence where he can expect more incursions into his private life, media consultants and analysts say, especially if he enters the presidential contest, in which the disclosure of even minor medical problems has become routine.

“My belief is it's wise for political candidates and officeholders to be open and honest about their medical history and conditions,” said Bob Steele, the Nelson Poynter Scholar for Journalism Values at the Poynter Institute.

“Especially for officeholders of any important position, because it's possible that a medical condition, even a previous condition that's been addressed, could have an impact on that officeholder's ability to serve the public.”

In addition, Mr. Steele said, in the age of the Internet, it is important for public figures to ensure that the information is correct, to let “the truth be the framework and the fodder for examination.”

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