Almost Erdős sets

Key Points

• To explore the conditions under which a decreasing null sequence can be classified as an almost Erdős set.
• Defined almost Erdős sets in terms of Lebesgue measure and linear transformations.
• Analyzed the behavior of decreasing null sequences with a decay rate greater than 1/2.
• Established criteria for nonempty subsets of S under Lebesgue measure.
• Demonstrated that any decreasing null sequence with a decay rate greater than 1/2 qualifies as an almost Erdős set.
• Provided examples illustrating the set properties that conform to the almost Erdős definition.